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Full text of "Effectiveness of alternative skid reduction measures : final report"

TE 
662 

.A3 
no. 

FHW/V- 
RD- 



jort No. FHWA-RD- 79-23 



/ 



v.-. FFECTIVENESS OF ALTERNATIVE 
SKID REDUCTION MEASURES 



DEPARTMENT OF 
TRANSPORTATION 

APR 2 1980 

LIBRARY 



Vol. II. Benefit-Cost Model 
November 1978 
Final Report 





Document is available to the public through 
the National Technical Information Service, 
Springfield, Virginia 22161 



Prepared for 

FEDERAL HIGHWAY ADMINISTRATION 
Offices of Research & Development 
Environmental Division 

Washington, D.C. 20590 



FOREWORD 



This report is part of a final report consisting of an executive summary 
and four volumes. The executive summary provides a synopsis of the 
research. Volume I describes the evaluation of accident rate -skid number 
relationships; Volume II describes the development of the benefit-cost 
model; Volume III presents the computerized benefit-cost model and 
instructions for its use; and Volume IV summarizes methods of measuring 
and achieving macrotexture. It will interest those concerned with 
pavement surface characteristics and the selection of accident reduction 
measures . 

This research is included in Project 1H, "Skid Accident Reduction" of 
the Federally Coordinated Program of Research and Development. 
Mr. George B. Pilkington II is the Project Manager and Mr. Philip Brinkman 
is the Task Manager. 

One copy of this report is being distributed to each FHWA regional office. 




Director, Office of Research 
Federal Highway Administration 



NOTICE 

This document is disseminated under the sponsorship of the Department of 
Transportation in the interest of information exchange. The United States 
Government assumes no liability for its contents or use thereof. The 
contents of this report reflect the views of the contractor, vho is 
responsible for the accuracy of the data presented herein. The contents 
do not necessarily reflect the official views or policy of the Department 
of Transportation. This report does not constitute a standard, specification, 
or regulation. 

The United States Government does not endorse products or manufacturers. 
Trade or manufacturers' names appear herein only because they are considered 
essential to the object of this document. 






ff-£3 



Technical Report Documentation Page 



1. Roport No. 

FHWA-RD-79-23 



2. Gov»ra!»«nl Accession Ho 



4. Title and SubtitU 

Effectiveness of Alternative Skid Reduction 

Measures. 
Volume II: Benefit-Cost Model 



7. a***.'.) a. D. St. John, R. 
D. W. Harwood 



R. Blackburn, and 



9. Perforating Organisation Nam* and Addross 

Midwest Research Institute 

425 Volker Boulevard 

Kansas City, Missouri 64110 



12. Sponsoring Agoney Narao and Addross 

U.S. Department of Transportation. 
Federal Highwav Administration] LIBRARY 
Offices of Research and Develo pment 
Washington, D.C. 20590 




3. Roci0i«n('s Catalog No. 



S. Rvport Data 

November 1978 



6. Pstrforngng Organization Coda 



8. Parrontung Organization Rapoct No. 

3824-D 



1,0. WoHi Umt No. (TRAIS) 

31H5-014 



\. Contract or Gran* No. 

D0T-FH-11-812Q 



13. Typo of Report and Ponod Co»«'*d 

Final Report 

June 1973-November 1978 



«4. Sponsoring Agancy Coda 

/£f O -^3 9 



15. Supplorattntory Noto* 

FHWA Contract Manager: P. Brinkman, BP.S-^3 



1*. Abstract 

A computerized benefit-cost model was designed for use by state highway 
departments in the selection of accident-reduction counter-measures to be 
applied to Investigated sites. Two types of wet-pavement accident reduction 
countermeasures are in current use: those that increase frictional supply 
and those that decrease frictional demand. Although this project emphasized 
countermeasures that influence skid number and wet-pavement accidents, the 
computerized model treats accidents under both wet- and dry-pavement condi- 
tions and, in addition, evaluates costs and benefits for geometric and traf- 
fic control countermeasures. Thus, the computerized model is a general pur- 
pose tool for the selection of accident countermeasures. The tables supplied 
with and employed by the model include the published accident reduction per- 
centages for most countermeasures currently employed. The model also in- 
cludes the relations between wet-pavement accident rates and skid number 
found in Phase I of this project. In addition, the model includes a novel 
treatment of highway user costs associated with construction zone activities. 
It provides as output, cost and benefit data that can be compared and used in 
budgeting. 



17. K«y Words 

Benefit-cost model Skidding accidents 

Skid number 

Wet pavement 

Accident countermeasures 



Computer programs 




19. SaCMfity Clwiul (of litis f O U T t ) 

Unclassified 



' 28. Seasrify Class*!, (oi this pogo) 

Unclassified 



14V Distribution Stptoraont ..,,, , . . « n . _ 

Document is available to the pubxic 
through the National Technical 
Information Service (HTIS). Springfield 
Virginia 22l6l. There is a charge for 
copies ordered from NTIS. 



21. No. of Pogos 22. Pnca 



236 



Fona DOT F 1700.7 («~72) 



PREFACE 



This draft final report was prepared by Midwest Research Insti- 
tute for the Federal Highway Administration under Contract No. DOT-FH-11- 
8120. Mr. Charles P. Brinkman of the Office of Research, Federal Highway 
Administration was the Contract Manager. 

The project benefited from the comments and suggestions of sev- 
eral other members of the staff of the Office of Research of FHWA includ- 
ing Mr. Ronald Giguere, Mr. George Pilkington, Ms. Julie Anna Fee, and 
Mr. Burton Stephens. In addition, the Data Systems Division of FHWA wrote 
all of the computer programs and made all computer runs for the project. 
We wish to thank Mr. William Mellott, Ms. Sandy Wallenhorst, Mr. Donald 
Clausen, and Mr.DavidWood of that division for their invaluable contri- 
butions. The actual computer programs and program listings are available 
from FHWA. 

We also wish to acknowledge the contributions of 16 state high- 
way and transportation departments and the following individuals who served 
as principal contacts for the project: Mr. Dave Henry of the California 
Department of Transportation, Dr. Charles E. Dougan of the Connecticut De- 
partment of Transportation, Mr. Thomas I. Bates of the Florida Department 
of Transportation, Mr. William C. Walters of the Louisiana Department of 
Highways, Mr. Wilbur Dunphy of the Maine Department of Transportation, Mr. F. 
Stanley Kinney of the Maryland State Highway Administration, Mr. Francis W. 
Holden of the Massachusetts Department of Public Works, Mr. Fred Copple of 
the Michigan Department of State Highways, Mr. Paul Teng of the Mississippi 
State Highway Department, Mr. Lee Webster of the North Carolina Department 
of Transportation, Mr. Leon 0. Talbert of the Ohio Department of Transporta- 
tion, Mr. John G. Hopkins, III of the Pennsylvania Department of Transporta- 
tion, Mr. Robert Fruggiero of the Rhode Island Department of Transportation, 
Mr. Billy R. Gibson of the South Carolina State Highway Department, Mr. R. V. 
LeClerc of the Washington State Highway Commission and Mr. John R. O'Leary 
of the West Virginia Department of Highways. Many other individuals in these 
agencies provided invaluable assistance which is gratefully acknowledged. 

The work reported herein was carried out in the Engineering and 
Economics and Management Sciences Divisions, under the administrative direc- 
tion of Dr. William D. Glauz. Mr. Robert R. Blackburn, Manager, Driver and 
Environmental Group; and Mr. A. D. St. John, Senior Advisor for Analysis, 
served as principal investigators for the study. Messrs. St. John and 
Blackburn, together with Mr. Douglas W. Harwood, Associate Traffic Engineer, 
were co-authors of this volume of the report. Mr. Jerry L. Graham, Asso- 
ciate Traffic Engineer, contributed to Appendix D; and Dr. Stan Soliday 
(formerly of MRI) contributed to Appendix H. Dr. William D. Glauz, Manager, 

ii 



Transportation Systems Section, contributed to the organization and editing 
of this volume of the report. Present and past members of the MR I staff 
who also contributed indirectly to the work reported include: Mr. Duncan I, 
Sommerville, Ms. Cathy J. Wilton, and Mr. Patrick J. Heenan. 



Approved for: 

MIDWEST RESEARCH INSTITUTE 




(XmM' 



A. E. Vandegrift, Dirte&to^ 
Economics and Management 
Science Division 



L1X 



TABLE OF CONTENTS 

Page 

I. Introduction 1 

II. Benefit-Cost Model Scope and Application 4 

III. Support System 7 

IV. The Benefit-Cost Model — An Overview 10 

A. Model Attributes 10 

B. Two Steps --Economic Feasibility and Project 

Formulation. •• 11 

C. Overall Program Logic 12 

V. Major Components and Concerns of the Model 15 

A. Terminology 15 

B. Benefit/Cost Ratio 16 

C. Compound Interest Forms 16 

D. Period of Analysis and Applied Life 17 

E. Forms for Capital Costs and Benefits 19 

F. Capital Outlays 21 

G. Final Capital Worth 21 

H. Prior Decisions. • 22 

I. Right-of-Way Costs 23 

J. Weight Factors for Certain Costs .... 24 

K. Accident Severities and Costs 25 

L. User Costs 26 

M. Maintenance and Operating Expenses ... 26 

N. Traffic Volumes 27 

0. Skid Numbers 2 9 

VI. Accident Rates and Countermeasure Effects .... 31 

A. Results From Analyses of Skid Number and Accident 

Rates 31 

B. Basic Equations Depicting Skid Number-Accident 

Rate Relationships 34 

C. Graphical Visualization of Countermeasure Effects. 37 

D. Forms Employed In the Model. 39 

E. Macrotexture - Accident Rate Relations 43 

F. Accident Rates Associated With Geometric and 

Traffic Control Countermeasures 44 

G. Influence of ADT on Accident Rate. ........ 61 

H. Sequence of Processing Accidents and Accident 

Costs 61 

iv 



TABLE OF CONTENTS (continued) 

Page 

VII. Subscript Ranges for Counter-measures. 65 

VIII. Input Requirements 67 

A. General Input Data ........... 67 

B. Site Characteristics • 75 

C. Countermeasures. 75 

IX. Summary of Output 77 

A. Heading Block 79 

B. Comparisons of Base and Alternate Conditions ... 81 

X. Example of Benefit-Cost Analysis. . 84 

A. Example Problem. 84 

B. Input Data for Example Problem 35 

C. Output Data for Example Problem 93 

XI. Tests of the Computerized Model 95 

XII. Conclusions 98 

XIII. Recommendations 100 

Bibliography • • 101 

Appendix A - Potential Skidding-Accident Countermeasures 107 

Appendix B - Skid Resistance Change with Traffic Passages in the 

Benefit-Cost Model 115 

Appendix C - Accident Costs •• 125 

Appendix D - Additional User Costs Due to Construction 130 

Appendix E - Flow Diagrams and Specifications for Benefit-cost 

Program 162 

Appendix F - Subroutine Hierarchy 198 

Appendix G - Symbol Names and Definitions ..... 200 

Appendix H - Controlling Skidding by Influencing Driver Behavior. . . 216 

v 



TABLE OF CONTENTS (continued) 

List of Figures 

Figure Title Page 

1 Benefit-Cost Program Operation 6 

2 Maintenance of Support System 8 

3 Benefit-Cost Flow Diagram 13 

4 Rate of Change of Wet-Pavement Accident Rate with Skid Num- 

ber As a Function of Dry-Pavement Accident Rate for Rural 

Highways* . • • • • 32 

5 Relation Between Dry-Pavement and Wet-Pavement Accident 

Rates 36 

6 Overall Rural Accident Rate Versus Dry-Pavement Accident 

Rate and Skid Number, When Pavement is Wet 10% of Time. . 38 

7 Overall Rural Accident Rate Versus Dry-Pavement Accident 

Rate and Skid Number, When Pavement is Wet 30% of Time. . 38 

8 Format of Printed Output 78 

9 Output from Economic Feasibility Stage for Example Problem. 92 

10 Output from Project Formulation Stage for Example Problem . 94 

11 Two -Way, Two-Lane Highway Reduced to One Lane (Configura- 

tion 1) 136 

12 Stopped Delays, Configuration 1 for Volumes up to 1,400 vph 141 

13 Stopped Delays, Configuration 1 for Volumes of 1,400 to 

1,700 vph 142 

14 Stopped Delays, Configuration 1, Rural 143 

15 Stopped Delays, Configuration 1, Urban. 144 

16 Multilane Construction Zone Configurations 145 

17 Speed Capacity Relationships, Multilane ,Facili ties 148 



VI 



TABLE OF CONTENTS (continued) 

List of Figures 

Figure Title Page 

18 Vehicle-Hours of Delay Due to Reduced Speeds (Configura- 

tion 2) 150 

19 Delays Due to Reduced Speeds, Configuration 2, Urban. . . • 151 

20 Excess Fuel Consumption, Configuration 1, Urban 155 

21 Excess Fuel Consumption Due to Speed Change Cycles, Con- 

figuration 2 153 

22 Excess Fuel Consumption Due to Reduced Speed, Configuration 

2 159 

23 Excess Fuel Consumed, Configuration 2. .......... 160 

24 Benefit-Cost Flow Diagram 169 

25 Subroutine PREPl Flow Diagram 170 

26 Subroutine PREP2 Flow Diagram 172 

27 Subroutine ADT Flow Diagram 174 

28 Subroutine SIG Flow Diagram 175 

29 Subroutine ALIFE Flow Diagram 176 

30 Subroutine FCAPW Flow Diagram 177 

31 Subroutine EACC Flow Diagram 178 

32 Subroutine EFEAS Flow Diagram 179 

33 Subroutine PFRM Flow Diagram 180 

34 Subroutine BOC Flow Diagram 181 

35 Subroutine C0STS(JJ) Flow Diagram 183 

36 Subroutine SETCST Flow Diagram 184 



VI 1 



TABLE OF CONTENTS (continued) 



List of Figures 



Figure Title Page 

37 Subroutine SKIDI Flow Diagram 185 

38 Subroutine C0RRT Flow Diagram 186 

39 Subroutine GREDU Flow Diagram 187 

40 Subroutine DT0UR Flow Diagram 189 

41 Subroutine SNADJ Flow Diagram 190 

42 Subroutine CALCST Flow Diagram 191 

43 Subroutine SKIDC Flow Diagram I 92 

44 Subroutine DTADJ Flow Diagram 193 

45 Subroutine ACC0ST Flow Diagram ..... * 9 ^ 

46 Subroutine YRM0 Flow Diagram 

47 Subroutine YRAC Flow Diagram 

48 Subroutine DC0STS Flow Diagram 



196 
197 



vm 



TABLE OF CONTENTS (continued) 
List of Tables 

Table Title Page 

1 Regression Coefficients, b and bi. ........... . 35 

2 Average Skid Numbers at 40 MPH (64 KM/HR) 35 

3 Regression Coefficients, a Q and aj 37 

4 Summary of Coefficients for Equations Employed in Model . . 41 

5 Geometric and Traffic Control Countermeasures Incor- 

porated in the Model 45 

6 Values of ax and b^ Used to Determine Correction 

Factor, G 55 

7 Illustrative Values of the Correction Factor, G ..... . 56 

8 Distribution of Accident Severities by Highway Type 

and Area Type 59 

9 Distribution of Accident Types by Area Type and Site Type . 60 

10 Coefficients and Limit ADT for AJDT 62 

11 Input for Benefit-Cost Program. •••.".......... 68 

12 Input Data Supplied by User for Example Problem ...... 86 

13 Partial List of Data from System Files for Example 

14 Features and Options Checked in Preliminary Tests ..... 96 

15 Distribution of Accident Severities ............ 128 

16 Coefficients for Accident Cost Equations. ......... 129 

17 Area Type - Closure Schedule Combinations ......... 131 

18 Coefficients* for Delay Equation (Configuration 1) 131 



IX 



TABLE OF CONTENTS (continued) 
List of Tables 

Table Title Page 

19 Coefficients for Excess Fuel Consumption Equation 

(Configuration 1) 132 

20 Coefficients for the Delay Equation (Configuration 2). . . 134 

21 Coefficients for Excess Fuel Consumption Equation 

(Configuration 2) 135 

22 Reduced Speed Delay Factors 139 

23 Delays from Reduced Speeds (Configuration 2)....... 149 

24 Delays Due to Stoppage in Queules and Reduced Speeds 

During Queue Dissipation for Configuration 2 152 

25 Excess Fuel Consumption, Configuration 1 l^ 7 

26 Additional Initial Values to be Set in Subroutine PREP1. . 171 

173 



27 Tests and Messages for Subroutine PREP2 

28 Code Definitions for Symbols 

29 Symbol Names and Definitions . . • . • 



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XI 



I. INTRODUCTION 



Slippery pavements have existed since the advent of the paved 
highway, but the causes of slipperiness, its measurement, and its in- 
fluence on traffic accidents were not of great concern before 1950. Al- 
though reliable data have been difficult to find, recent research sug- 
gests that skidding accidents are increasing rapidly and are reaching 
proportions that can no longer be ignored. One researcher— has indi- 
cated that skidding accidents account for more than one-third of all 
vehicle accidents in some geographical areas. This trend is undoubtedly 
a reflection of increased vehicle speeds and traffic volumes. 

Each year our highways are used by more vehicles traveling at 
increased speeds. The increased traffic volumes have reduced the average 
headway between vehicles, and this reduction, in combination with increased 
speed, has reduced the time and distance available to the driver to avoid 
collison circumstances. 

More rapid accelerations, higher travel speeds, and more severe 
braking made possible by modern highway and vehicle designs have raised the 
frictional demands on the tire-pavement interface. Larger forces are re- 
quired to keep the vehicle on its intended path. On the other hand, for 
wet pavements, the frictional capability of the tire-pavement interface 
decreases with increasing speed. In addition, higher traffic volumes and 
speeds promote a faster degradation of the frictional capability of the 
pavement . 

The tire-pavement friction level at which skidding is imminent 
depends mainly on the speed of the vehicle, the co: ring path, the magni- 
tude of acceleration or braking, the condition of the tires, and the char- 
acterises of the pavement surface. On wet pavements, speed is the most 
significant parameter, not only because frictional demand increases with 
the square of the speed, but also because the skid resistance of the tire- 
pavement interface decreases with increasing speed. 

Skidding accidents constitute a significant traffic safety problem, 
especially on highways with high vehicle speeds and high traffic volumes. 
Timely steps should be taken to ensure compatibility between frictional de- 
mands and available skid resistance. From the technological standpoint, the 
skidding accident problem is amenable to solutions that either reduce the 
frictional demand (such as improved geometric design and wet-weather speed 
limits), or increase the skid resistance (improved pavement texture and 
drainage, improved tire design, and more stringent vehicle inspection con- 
trols) • 



The Federal Highway Administration is cognizant of the skidding 
accident problem and has undertaken a multidirectional safety research ef- 
fort aimed at the reduction of wet-pavement accidents. The Administration 
is coordinating complementary research directed at: (1) evaluating the 
mechanical interaction of the tire-pavement interface, (2) determining 
the frictional demands of traffic, (3) relating wet-pavement accident 
rates to available skid resistance, and (4) combining all traffic, en- 
gineering, and economic factors in a cost-benefit model. This coordinated 
approach has promise to successfully achieve its goal of establishing com- 
prehensive skid resistance requirements that can be implemented to com- 
pare locations and select appropriate countermeasures subject to funding 
constraints. 

This is the final report on a project (Contract No. DOT-FH-11- 
8120) concerned with the third and fourth of the above goals of the FHWA 
approach to the wet-pavement accident problem. The project consists of 
two phases, corresponding to the two major objectives of the project: 

1. To develop the relationships between pavement skid number 
and wet-pavement accidents for a variety of highway and traffic conditions 
(Phase I). 

2. To define and evaluate, on a cost-effectiveness basis, a 
range of alternative solutions to the problem of maintaining the fric- 
tional requirements of drivers during wet weather (Phase II) . 

The final report is divided into four volumes. Volume I de- 
scribes the work conducted and results obtained under Phase I; Volume II 
pertains to the work performed under Phase II; and Volume III is a user 
manual describing the benefit-cost model developed under Phase II and the 
instructions for the model use by state highway departments. Volume IV is 
a guide to the subject of pavement macrotexture. It discusses the impor- 
tance of pavement macrotexture in reducing skidding accidents and describes 
the methods of measuring pavement macrotexture, and the techniques for pro- 
viding macrotexture in new pavements and restoring macrotexture in existing 
pavements. Volume IV also applies a simplified version of the benefit-cost 
approach presented in Volumes II and III to the evaluation of alternative 
pavement macrotexture improvements. 

The results reported in this volume cover the Phase II activities. 
This phase involved the identification of potential effective countermeasures 
for wet-pavement accidents, the development of a comprehensive computerized 
benefit-cost model to evaluate those countermeasures, the development of a 
computerized system to support the benefit-cost model, the assembly of a 
data base for the model, and the applied demonstration of the model. 



The Federal Highway Administration's Data Systems Division per- 
formed all of the computer programming for the benefit-cost model and its 
support system, the data system management, and the program execution. 
Midwest Research Institute provided FHWA with program specifications, logic 
descriptions, and flow diagrams at various levels of detail. The actual 
programs and program listings are available from FHWA. 

This volume is organized in the following manner. Section II 
describes the scope and application of the benefit-cost model. The com- 
puterized support system for the model is discussed in Section III. An 
overview of the computerized benefit-cost model is described in Section 
IV. This is followed by a description in Section V of the major compon- 
ents and concerns of the model. Section VI presents a discussion of acci- 
dent rates: their relationship to skid number and associated variables 
(drawn from the results of Phase I); their association with geometric and 
traffic control measures; and the way the relations are incorporated in the 
model. The subscript ranges dealing with the countermeasures employed by 
the computerized benefit-cost model and its support system are given in 
Section VII. A summary of the model's input requirements and output for- 
mat are discussed in Sections VIII and IX, respectively. Section X pre- 
sents examples of the benefit-cost model while tests of the model are 
given in Section XI. The conclusions of the Phase II activity are pre- 
sented in Section XII followed by the recommendations in Section XIII. 

Eight appendices are given at the end of this report. These 
present discussions of the following topics: potential countermeasures 
for skidding accidents, skid numbers, accident severities and costs, added 
user costs during construction, flow diagrams for the computer programs, 
subroutine hierarchy, the symbol names used in the computer programs, and 
means of controlling skidding by influencing driver behavior. 



II. BENEFIT-COST MODEL SCOPE AND APPLICATION 



The computerized benefit-cost model is designed for use by state 
highway departments in the selection of accident-reduction countermeasures 
to be applied to investigated sites. Two types of wet-pavement accident 
reduction countermeasures are in current use: those that increase fric- 
tional supply and those that decrease frictional demand. Although this 
project has emphasized countermeasures that influence skid number and wet- 
pavement accidents, the computerized model treats accidents under both wet- 
and dry-pavement conditions and, in addition, evaluates costs and benefits 
for geometric and traffic control countermeasures. In fact, it is essential 
for the model to treat both types of countermeasures since they must be 
evaluated in competition with one another for selection of countermeasures 
with the most favorable benefit/cost ratios. Thus, the computerized model 
is a general purpose tool for the selection of accident countermeasures. 
The tables supplied with and employed by the model include the published 
accident reduction percentages for most countermeasures currently employed. 
The model also includes the relations between wet-pavement accident rates 
and skid number found in Phase I of this project. 

The model makes use of engineering judgement by examining only 
those countermeasures for a site that the user specifies with input data. 
The specified countermeasures are examined, first, in comparison to the 
"as is" or "as planned" conditions for the site. Those countermeasures 
found to be economically feasible are then compared with one another to 
identify the countermeasure with the best benefit/cost ratio. Printed 
output is provided for the economic feasibility results and for the sub- 
sequent comparisons that are frequently described as project formulation . 
The printed output contains the important economic and safety variables 
useful for decision making. In this regard it is recognized that the model 
deals individually with each potential site for countermeasure application. 
Ultimately, in budgeting, sites must be considered in competition for the 
best distribution of countermeasure funds. The model does not deal expli- 
citly with this site-to-site competition, but instead provides printed re- 
sults for each site that can be compared and used in budgeting. 

The computerized model currently examines countermeasures indi- 
vidually. The logical organization of the model could be extended to 
evaluate multiple countermeasure options, but it does not presently have 
the capability to evaluate the benefit-cost ratio for such combinations 
of countermeasures. 

In the development of the computerized model, emphasis has been 
placed on compatibility with normal highway department practices and on 
accurate quantification of accident and economic consequences. The model 
provides accurate evaluations of accident and economic aspects in cases 



where: (1) a prior decision has been made to modify the analyzed site; 
(2) future resurfacing or rebuilding will influence the life of counter- 
measures; (3) right-of-way must be acquired for a countermeasure ; (4) the 
ADT will change drastically in the future due to the addition of continuing 
segments or parallel facilities; or (5) the facility will be abandoned in 
a future year. Current practice most frequently employs approximations or 
engineering and economic judgement to account for the above factors; the 
computerized model handles them explicitly. 

The computerized benefit-cost model utilizes auxiliary data files . 
that supply standard values for such items as countermeasure costs and acci- 
dent reductions, and the distributions of accident severities and accident 
costs. A support system of a computer program provides procedures for a state 
highway department to incorporate and update the values of these items. In 
addition, the user in the highway department is given the option of supply- 
ing overriding values in individual calculations. 

Figure 1 shows the elements involved when the benefit-cost model 
is executed. The details of that program are presented beginning with 
Section IV of this report. The support system and file maintenance are 
described first, in Section III. 

The remainder of this report concentrates on the work performed 
by MRI, but recognizes the coordinated efforts of FHWA's Data Systems 
Division, which performed all of the computer programming, data system 
management, and program execution. The coordination was accomplished by 
MRI's provision of program specifications, logic descriptions, and flow 
diagrams at various levels of detail. For each program or segment, the 
level of detail was selected to leave maximum latitude for the programming 
and data system management, while simultaneously providing great detail 
where necessary to ensure incorporation of the correct logic. Examples 
of the extremes are found in the very general specification of the support 
system, as contrasted with the detailed specification of logic for certain 
routines in the benefit-cost computer program. This report reflects the 
specifications provided. The actual programs and program listings are 
available from FHWA. 



User's 

Data 

Input 



Benefit- 
Cost 
Program 



Results 



r 



Support System 



User's Data 
for File 
Generation 
and Update 



Files 





Figure 1 - Benefit-Cost Program Operation 



III. SUPPORT SYSTEM 

The functions and capabilities of the support system are: 

1. The support system is used to update cost data files. 

2. The support system provides a printed listing of the updated 
and replaced cost data. 

3. The printed listing is useable to manually verify the new cost 
data and, subsequently, provide a document for record and reference. 

4. Cost data in the federally demonstrated system can be specific 
for individual states, and for cost centers within states. (When the system 
is used in a state highway department, cost data can be specific for each 
regional cost center of the state.) 

5. The system provides the correct cost data files to the benefit- 
cost program in response to the input on state and region associated with 
each case analyzed. 

Figure 2 shows the process of updating (maintaining) the support 
system cost files. The process includes the provision of new cost data for 
the files, the incorporation of these new data in the files, the generation 
of listings of the files and changes, and manual verification of the changes. 

Three other capabilities for the support system may have utility 
in continued application but were not needed in the development activities 
of this project. These three capabilities are described below. 

1. A permanent file sequenced by case number could be generated, 
where a case is one analysis of one or more alternatives. (A case number 
should be assigned even if the analysis is terminated after the preliminary 
computations in the benefit-cost model indicate that significant accident 
savings cannot be achieved. A case number should not be assigned when 
analysis is terminated due to incorrect or incomplete input data.) The 
system should transmit the next case number to the benefit-cost program. 
The sequential file should include the case number, and numerical codes 
for the date of analysis, the type of facility, the feature, i.e., inter- 
section, curve or section, the climatological coefficients (up to three) 

and the location information which includes the state, the state subdivision, 
and the milepost limits. 

2. The case file could be updated with decision and implementa- 
tion data. The decision information is the date of decision and the selected 
countermeasure type (including none) . The implementation date is the date 
when the countermeasure is completed and in use. 



Fi les are for: 

• Capital Cosrs 

• Accident Reductions 

• Accident Types 

• Maintenance & Operation Costs 

• User Costs 

• Accident Costs 

• Normal Service Lives 

• Net Salvage Values 

• Costs of Removal and 

• Interest Rates Employed 
Files are Expected to be Moderate 
in Size so thar Manual Verification 
of New Values will be an Acceptable 
Procedure. 

* Documentation, Procedures, and 
Decisions Performed by User. 





Previous Cost 
Listing 



Changed 
Costs * 




No 



Card to 
Tape 




Update 




Edit 




Release Old 

Cost Tape 

\& Change/ 

Cards 



End of One 
Update Cycle 



Old, New 
Listing with 
Flags 



Listing Contains Abbreviated Names 
Changed Values are Flagged. 
Changes Exceeding Threshold % are 

Double Flagged. 
Accepted Version is Retained by 
User to Document Values in Use and 
to Prepare Next Uodate. 



Figure 2 - Maintenance of Support System 






3. The third capability would delete unused countermeasures , 
and/or add new countermeasures in limited numbers. Printed output should 
document the revisions and dates of revisions. 



IV. THE BENEFIT-COST MODEL—AN OVERVIEW 



The benefit-cost model was designed to be implemented as a com- 
puter program. Thus, unless specifically stated otherwise, references to 
the model apply equally to the program, and vice-versa. 

This overview begins with a discussion of the fundamental attri- 
butes of the model. Next, the basic two-step concept utilized in examining 
alternative countermeasures to wet-pavement accidents is discussed. Finally, 
the overall flow diagram is presented and described briefly. Further details 
are reserved for Section V, subsequent sections, and the appendices. 



A. Model Attributes 

The main attributes of the model (and the supporting system) are 
set by the envisioned applications. The model will be applied to evaluate 
countermeasures intended primarily to provide, as benefits, reduced costs 
of wet-pavement accidents. However, the model deals with total accidents 
and includes the capability to calculate benefits and costs for accident 
countermeasures in general. 

The model (and the computer program) are intended for use by 
state highway department personnel. Consequently, emphasis is placed on 
employment of information likely available, and compatibility with proce- 
dures employed by state highway departments. 

The attributes and capabilities of the benefit-cost model are 
listed below. 

1. The model is compatible with typical highway department or- 
ganization and procedures. (Primarily, this means accounting for the con- 
sequences of prior decisions on abandonment, resurfacing, or rebuilding 
where the decisions were motivated mainly by factors other than wet- 
pavement accidents.) 

2. The model provides both economic analysis and project for- 
mulation analysis. Economic analysis evaluates the economic feasibility 
of alternatives, and project formulation compares those alternatives found 
to be economically feasible. 

3. The model is organized to facilitate the analysis of conven- 
tional countermeasures with minimal user input. 

4. The program accepts unconventional countermeasures with user- 
oriented input. 



10 



5. The program accepts a list of specified countermeasures for 
analysis. 

6. There are two conventional methodologies for comparing alter- 
natives with unequal lives. Each method has value. The program uses one 
method as a standard and provides an option for the user to request the other. 

7. The program provides a convenient way for the user to modify, 
for individual cases, the costs of accidents and values of time. (These costs 
and values are frequently questioned.) 

8. The computer program employs modular blocks to facilitate changes 
to the logic and to numerical values. 

9. The computer program combined with other system elements is 
able to run several problems in succession. 

10. The computer program provides printed output for each case 
that can be used in planning and budgeting decisions, and subsequently as 
a permanent record of the results of analysis. 



B. Two Steps — Economic Feasibility and Project Formulation 

The principal measure of effectiveness used in the model is the 
benefit/cost ratio. Using this ratio, an analysis is performed in two steps 
In the first step each countermeasure is compared with a base condition, 
which is the "as is" or "as planned" condition for the facility. Counter- 
measures that provide a B/C ratio of one or more are judged to be economi- 
cally feasible. If more than one countermeasure is judged economically 
feasible, a second step is undertaken to identify the best of the feasible 
countermeasures . 

The second step is called project formulation or incremental 
analysis. The first operation for this step is to rank the economically 
feasible countermeasures in order of increasing capital costs. Then, the 
first-ranked countermeasure (lowest capital cost) is taken as the base 
and the next ranked countermeasure is taken as a challenger. If the re- 
sulting (incremental) B/C ratio is equal to or greater than one, the chal- 
lenger is accepted and becomes the base countermeasure in a calculation 
with the next ranked countermeasure. On the other hand, if the ratio is 
less than one, the challenger is discarded, and the base countermeasure is 
retained for comparison with the next ranked challenger. This process 
continues until each economically feasible countermeasure has challenged 
and has either been accepted or discarded. 



11 



There are three special aspects of the above sequence that influ- 
ence the operation of the benefit-cost program. First, the project formu- 
lation calculations are needed only if more than one countermeasure is found 
to be economically feasible. The test for this possibility is made in the 
main program. 

Second, it is recognized that the program does not make final 
decisions for a highway department. This is especially true in the project 
formulation calculations where, although the results always lead to the 
countermeasure yielding the most benefit per capital cost dollar, the se- 
quence progresses through countermeasures with successively larger capital 
costs.- Since, realistically, budget constraints are usually present, a 
final decision rests with the management and administration of the highway 
department. The cost-benefit program provides information useful in reach- 
ing that decision. Therefore, each calculation of both the economic analysis 
and the project formulation (if needed) are printed as an aid in decision 
making and subsequent review. 

Third, it is apparent that the form of the calculations and the 
results are similar in the two steps — economic analysis and project formu- 
lation. The same headings and print formats are thus appropriate for both. 
The only difference is in the main heading. Also, each calculation involves 
three elements: a base condition, either a countermeasure or a challenger, 
and differences reflected in the benefit/cost ratio (and other measures) . 
These three elements lend themselves to three lines of printed output for 
each calculation. 



C. Overall Program Logic 

The major routines of the benefit-cost computer program are shown 
in the flow diagram of Figure 3. The notes in the figure describe the gen- 
eral course of computations. 

One pass through the logic diagrammed in Figure 3 completes the 
benefit-cost analyses of all requested countermeasures at one highway site 
or section. The early routines read input information, obtain data from 
the support system files, and initialize variables. The next routines 
calculate for each requested countermeasure its applied life, its final 
capital worth, and capital costs at the highway site analyzed. 

Routine EFEAS conducts the economic feasibility analysis by com- 
paring the consequences with each requested countermeasure against the 
consequences with the "as is" or "as planned" conditions at the site. All 
the results are printed, and each countermeasure that provides a benefit/ 
cost ratio of one or more is accepted as economically feasible. If two or 
more countermeasures are economically feasible the program continues by 
employing routine PFRM. 

12 




©- 



Pint cord contain* r'.STAT, KSTAR. FA'ET APREC wh.ch ore »^e STATE CODE. 
th« STATE REGION CODE. •*• FACTION TIME WET PAVEMENT, and 

AVENGE ANNUAL PRECIPITATION (inc^esj. 



Blonk card terminates t\jn. 



Set tome subscripted variables = 0. 
„*.-" Read required filet into memory. 

Set variables 'o standard initial values. 



Read remoinder of input data for 
^ -^ one cose including alternatives for 

weight factor? and periods of analysis. 



^^ Calculate AADT 



CALL ACCOST 




Determine if significant accident 
savings are possible. 



^m *" Print basis for non-significant savings. 



Calculate applied lives, final capitol 
worths, and equivalent uniform 
annual capital costs. 



Calculate and print results of 
economic feasibility analyses. 



CALL PFRM 



Calculate end print results of 
project formulation analyses. 




NVAR = NVAR + I 



\- 



Advance subscript for next period 
of onolysis and weight factors. 



Figure 3 - Benefit-Cost Flow Diagram 

13 



Routine PFRM conducts the project formulation analysis by testing 
one economically feasible countermeasure against another. The procedure 
starts with the countermeasure that has the smallest capital cost and chal- 
lenges that countermeasure with the countermeasure with the next higher cost. 
Challenging countermeasures that exhibit an incremental benefit/ cost ratio 
greater than one are accepted and used in subsequent incremental analyses 
against next higher cost countermeasures. The results of all incremental 
analyses are printed. This concludes the benefit-cost analysis of the high- 
way site with the user-specified countermeasures. 

The test on MVAR-NVAR is part of an option to repeat the analyses 
at the same site, using the same countermeasures but with a different period 
of analysis and/or different accident cost values. 

The computer model contains some logical elements that are not 
very well-defined by currently available data. These elements have been 
given analytical forms that permit the use of best estimates and are also 
convenient for making sensitivity tests. 



14 



V. MAJOR COMPONENTS AND CONCERNS OF THE MODEL 



In this section are discussed the main aspects of the beneift-cost 
model, other than accident probabilities and their relationships to various 
countermeasures , which are the subject of Section VI. 

The computer program terminology is described in Section A, and 
the philosophy behind and equation for the benefit/cost ratio are given in 
Section B. Several features of an economic nature, means of defining and 
apportioning costs, etc, are presented in Sections C through G. The effect 
of prior decisions to rebuild or otherwise modify a highway facility, and 
how the program handles these decisions are presented in Section H. The 
subject of the cost of right-of-way is treated in Section I. Section J 
explains how the model provides flexibility in dealing with particular costs 
of a controversial nature--the costs of accidents, including injuries and 
fatalities, and the value of time and delays. The means of treating accidents 
of various severities, and the file data furnished relative thereto, are de- 
scribed in Section K. User costs imposed by construction associated with 
countermeasure implementation are discussed in Section L. Maintenance and 
operating expenses associated with the countermeasures are in Section M, 
and traffic volume estimates and their change in time are described in Sec- 
tion N. Finally, a review of the relationships between skid number and fac- 
tors such as material properties, traffic volume, and aging is given in Sec- 
tion 0. 



A. Terminology 

Many of the following portions of this and subsequent sections deal 
with details of the computer program logic. Reference to the flow diagrams 
in Appendix E (and the actual program listings) is simplified by utilizing 
the same symbols and names in the discussion. The symbols and names, which 
are suggestive of their functions, are generally defined where first used 
in the discussion. Appendix F contains a complete listing (with definitions) 
of these names. 

The program, written in FORTRAN IV, makes extensive use of sub- 
scripted variables. They are identified in the program and in the discussion 
as a symbol name followed by the subscript in parenthesis. Thus, FCW(KM) 
is the final capital worth of countermeasure KM, where KM identifies a spe- 
cific countermeasure of a series being examined. The notation FCW( ) is 
used to signify the entire array of values of final capital worths. 



15 



B. Benefit/Cost Ratio 

The ratio of benefits to costs is used as the main measure of 
countermeasure effectiveness. In general, it is defined as the fraction 
(using non-computer terminology): 

AC b - AC C + M0 b - M0 C + UC b - UC C , 

B/C = 

cc c - CC b 

where AC = Accident costs 

MO = Maintenance and operating costs 

UC = User costs 

CC = Capital costs, and 

subscript b indicates the base condition, while 

subscript c indicates the condition with countermeasure. 



In the program formulation step, the subscript b refers to the base coun- 
termeasure and c refers to the challenging countermeasure. 

Experts are not in agreement on the location in the fraction of 
the MO and UC terms. We follow Winfrey, 21/ placing the terms in the nu- 
merator. With this form the denominator contains capital costs exclusively. 



C. Compound Interest Forms 

The compound interest forms used in the model logic are based on 
year-end cash flows. That is, all payments, receipts, and benefits are 
treated as though they occurred at the end of each year. The discount fac- 
tor l/(l+i) n is used to obtain the present worth of a single amount n 
periods (years) in the future with interest rate i (a decimal, such as 
0.06). The capital recovery factor is [i (l + i) n ]/[(l + i) n - 1]. It is 
used to convert a present capital worth (when the countermeasure is installed 
prior to the beginning of the first year) to the equivalent uniform annual 
capital cost over a life of n years at interest rate i . 



16 



Winfrey has coined the word, vestcharge, to describe the interest 
rate employed in economic analyses of investments in public works. The sym- 
bol name V has been employed in the flow diagrams for this interest rate. 
The symbol name VI is employed for V + 1.0 . 

In the computer program a standard rate VS is obtained from the 
data files and V is set equal to VS in subroutine PREPI. The program 
user may provide another value for V to be read in subroutine REED. 



D. Period of Analysis and Applied Life 

Several problems arise in selecting a period of analysis and 
making an equitable comparison between alternatives that have different 
lives. However, before this question can be addressed, it is necessary to 
examine the practical aspects that determine the life of a countermeasure. 

According to normal economic practice, the life of a countermea- 
sure would be the number of years that the principal capital cost items 
would last while serving their intended purpose. However, in the present 
application, it is necessary to recognize that additional factors may limit 
this time period. As a simple example, consider a highway section that is 
scheduled for resurfacing at the end of 2 years, to restore the riding qual- 
ities and weather-resisting properties. A surface treatment with a normal 
service life of 3 years could be applied now to improve skid number. How- 
ever, the skid number improvement would be realized for a maximum of only 
2 years. The phrase "applied life" has been adopted here to describe the 
period that the countermeasure capital item(s) will actually be employed 
for their intended purpose. Applied life may equal but not exceed normal 
service life. In this example, the applied life is 2 years. 

There are several types of future actions and normal expectations 
that may reduce the applied life of a countermeasure below its normal ser- 
vice life. They are: 

Plans to resurface in a future year (applied life is normal 
i remaining life of present surface course). 

Plans to rebuild in a future year (applied life is normal 
remaining life of present facility). 

Plans to abandon facility in a future year (applied life is 
normal remaining period of operation of facility). 

All countermeasures are not equally vulnerable to future actions. 
A code has been devised to describe vulnerabilities, and logic has been de- 
vised to determine applied lives. The logic is applied in subroutine ALIFE 
where the applied life of each countermeasure is calculated for the site 

17 



under study. However, the program user may specify the applied life of 
individual countermeasures and override the file values and Logic normally 
used. To provide this option the subscripted values of applied life, LAF( ), 
are set equal to zero in subroutine PREPI; values supplied by the program 
user are read in subroutine REED; and subroutine ALIFE tests the LAF( ) 
values individually for user input before employing normal computational 
logic. Similar options are provided the program user for other quantities 
described subsequently, such as final capital worth and capital cost. 

In the analyses for economic feasibility each count ermeasure is 
compared with the base condition--the "as is" or "as planned" condition. 
In these analyses the periods of analysis are taken as the applied life of 
the count ermeasure. The applied life includes the effects of future plans 
for the facility. 

When two alternatives with unequal applied lives are compared a 
period of analysis must be chosen and employed. Winfrey recommends a period 
of analysis equal to the shorter of the two lives. He argues that predic- 
tions for the near term are more certain and that for the shorter-lived al- 
ternate, another option is possible at the end of the period. Economists 
seem to prefer the longer period and assume that the shorter-lived alter- 
nate recycles. 

In the present application there does not appear to be a "right" 
choice for period of analysis. The longer-lived alternate may exhibit en- 
hanced benefits in the future due to traffic growth and the characteristics 
of the countermeasure. If the shorter period is chosen, the longer-lived 
alternate may be unfairly penalized. If the longer period is chosen, it 
may be unfair or unrealistic to assume that the shorter-lived alternate goes 
through additional cycles. We meet this problem by taking the longer life 
as the standard period of analysis but provide the user with the option to 
request a second analysis that employs the shorter of the applied lives. 
Even if the analyses produce different results they will provide useful 
information for management decision making which can consider the confidence 
in projections used and the indicated burdens on current and future budgets. 

The symbol JPER( ) is used in subroutine PFRM as a code for selec- 
tion of period of analysis. A code value of 1 selects the shorter period; 
2 selects the longer period. The default value JPER(l) = 2 is set in sub- 
routine PREPI. That subroutine also initializes MVAR, the largest subscript 
to be employed for JPER( ), to the value, 1. The value of JPER(l) can be 
altered in subroutine REED, or the range of subscripts, MVAR, can be in- 
creased to include other options for both JPER( ) and the weight factors for 
costs described in Section E which also must be defined for the subscripts 
1 to MVAR. 



18 



The subscripts for JPER( ) and the cost-weight factors are part 
of an option to calculate benefit/cost ratios under more than one set of 
cost or time period estimates. When the subscript is given a range MVAR 
greater than one (in input), MVAR separate sets of calculations are made for 
the same site and set of counterrneasures. Each calculation set employs 
the JPER( ) and cost-weight factors supplied by the user for the associated 
subscript. 



E. Forms for Capital Costs and Benefits 

Authorities in economic analysis agree that in a comparison be- 
tween two alternatives the period analyzed (period of analysis) should be 
the same for both alternatives. However, in order to provide an equitable 
valuation of each alternative, the concept of equal periods is frequently 
carried out implicitly rather than explicitly. The calculation of capital 
costs is an example which is now described. 



siders: 



An equitable valuation of capital costs for a count ermeasure con- 

The initial capital outlay, COI 

The applied life, n 

The final capital worth, FCW, at the end of applied life, and 

The vestcharge or interest rate, i. 

The capital costs can be expressed in terms of their present 
worth, FWCC, by 



PWCC = COI - FCW-PW in * 

where ^in = l/(H"i) n > the present worth discount factor for n years 

at rate i . (i is expressed as a decimal, not as a 
percentage) . 



* This form assumes that the capital outlay COI is made immediately pre- 
ceding the beginning of the first year. This assumption is employed 
in all logic. 



19 



The capital costs can also be expressed on an annual basis as the 
equivalent uniform annual capital cost, EUACC , where 



EUACC = PWCG-CR. 
in 



and CR in = i (l+i) n /[ (l+i) n - 1] is the capital recovery factor for 

n years at interest rate i . 



Now, consider a period of analysis, m , which is shorter than the 
applied life n .* The equivalent uniform annual capital cost is still a 
fair valuation of capital costs since it has been placed on a per-year basis. 
However, the present worth of capital costs for the reduced period needs to 
be adjusted to reflect the remaining capital worth at the end of the shorter 
period, m . After the adjustment the valuations are equivalent; they differ 
only in form and units. It is important to note that with the shorter period 
of analysis neither of the forms for capital costs contains much information 
about the initial capital outlay. 

Because EUACC is unchanged by the period of analysis, the model 
employs the equivalent uniform annual capital costs. Consequently, the benefit/ 
cost ratio is formed as EUAB/ EUACC , where EUAB is the equivalent uniform 
annual benefit. Benefits are defined as (accident savings) - (increases in 
user costs) - (increases in maintenance and operating expenses), as noted in 
Section B. 

It is seen from the above that capital costs are adjusted implic- 
itly to periods shorter than applied life. In fact, the capital costs have 
an intrinsic cost/year character. One form, equivalent uniform annual cap- 
ital cost, does not change with the period analyzed. One might be tempted 
to treat benefits in a similar fashion so that the equivalent uniform annual 
benefits for each alternative would be independent of the analysis period. 
But the benefits may be greater or smaller in later years compared with 
earlier years. Thus, when equivalent uniform annual benefits are evaluated 
for compared alternatives over different periods, the comparison may not be 
equitable. Consequently, the benefits must be evaluated for compared al- 
ternatives over equal time periods. 

In summary, the equivalent uniform annual capital cost provides 
equitable valuations of capital costs even when applied lives of compared 
alternatives are not equal. But, to be equitable and comparable, benefits 
must be evaluated over the same time periods. 



This would be done if the count ermeasure is being compared with another 
having a shorter applied life. 



20 



F. Capital Outlays 

As indicated previously, when capital costs are transformed into 
equivalent uniform annual capital costs, the information about initial capi- 
tal outlays is obscured. Therefore, initial capital outlays and applied 
lives appear in the printed output from the computer program. The capital 
outlay is calculated in subroutine EACC as the product of UN(KM) , the number 
of units required, and either CAPC(KM) or SCAPC(KM), where CAPC(KM) is the 
capital cost per unit for countermeasure KM provided from the support system 
data file and SCAPC(KM) is an overriding value that can be supplied by the 
program user in subroutine REED. 



G. Final Capital Worth 

The capital cost items for a countermeasure have a final capital 
worth when the applied life ends. In the simplest case the final capital 
worth is the typical net salvage value. In other cases additional applied 
life may be realized by removing and reinstalling the capital cost items. 
Their final capital worth in the initial application is, of course, reduced 
by the cost for removal. Some capital items may have a final capital worth 
in place. An example is a surface course that is covered by resurfacing. 
The covered course may have structural value that persists and contributes 
to the life or load-bearing capabilities of the pavement. 

A code is employed in subroutine FCAPW to calculate final capital 
worth. The value of this code, TLR(KM), which is supplied from the data file 
for countermeasure KM, contains integer and fractional parts (Base 10). If 
the countermeasure capital items are disturbed by rebuilding, but not by re- 
surfacing, the integer part of TLR(KM) is 1, and the fractional part is the 
fraction of the then capital value that can be recovered during rebuilding. 
Again, that value is exclusive of the cost of removal, which is CR(KM) per 
unit capital item. If the countermeasure capital items are disturbed by 
resurfacing, the integer part of TLR(KM) is 2 and the fractional part is 
the fraction of the then capital value that can be recovered during resur- 
facing exclusive of costs of removal. When the integer part of TLR(KM) is 
2 and the facility is rebuilt, it is assumed that the final capital worth 
is equal to the net salvage value. 

The final capital worth for each unit of countermeasure KM, FCW(KM), 
can be entered by the program user as input read in subroutine REED. If 
the applied life LAF(KM) is directly supplied by the user for KM, then a 
non-zero value of FCW(KM) must also be supplied in input. If the final 
capital worth is zero or negligible, that fact should be indicated by in- 
puting the smallest positive quantity permitted by format. 



21 



H. Prior Decisions 

The model treats prior decisions in a simple and explicit way. 
(Here, a prior decision is a decision affecting the highway facility or 
traffic control that has been made but not carried out.) The base condi- 
tion takes the facility as it will be after prior decisions are carried out. 
This is similar to the attitude generally employed in benefit-cost analysis, 
where prior actions and their costs and consequences are irrelevant. How- 
ever, in this case, there is an opportunity to evaluate the comparative costs 
and benefits of alternatives that will implement the prior decisions and 
simultaneously reduce the likelihood of wet-pavement skidding accidents. 

Frequently the prior decision will be to resurface or rebuild. 
In these cases, the initial base condition must be the "as planned" condi- 
tion. The condition includes the new surface course. If alternative sur- 
face courses are considered as countermeasures, the alternatives should be 
charged capital costs only for the difference between the previously selected 
course and the alternative. (The difference in capital costs includes the 
effects of differences in service life, if any.) 

KLST( ) is a list of subscripts (pointers), identifying the spe- 
cific countermeasures contained in the support system file that are to be 
compared in an analysis. The initial base condition is always assigned sub- 
script 1, and KLST(l) = 1. Therefore, the prior decisions can be incorpo- 
rated in the description of the base condition as a part of input data for 
the case. It should be recognized that the capital costs for the base case 
will be employed only when an alternate surface course is considered as a 
countermeasure. If countermeasures other than alternate surface courses 
are considered, the capital cost for the base case will not be employed. 

Capital costs for the "as is" or "as planned" surface course may 
be employed whenever an alternate surface course is considered as a counter- 
measure. When there has been a prior decision to resurface (still subject 
to modification), the logic for economic feasibility charges the alternate 
surface course for its cost but also charges the "as planned" base condition 
for its planned capital costs. If the alternate surface course is found to 
be economically feasible, its capital cost is subsequently reduced to reflect 
the capital outlay already "sunk" in the "as planned" condition. This adjust- 
ment, which accounts for both costs and applied lives, is necessary so that 
the alternate surface course can compete fairly in project formulation 
against other countermeasures that do not involve surface courses. 

Capital costs for the "as is" surface course may enter the econ- 
omic feasibility calculation when a surface course countermeasure is con- 
sidered. The "as is" capital costs enter only when the life of the counter- 
measure course will extend beyond the future year when the "as is" course 



22 



would be replaced. In this case a fair comparison requires an account of 
the future outlay required for the "as is" base case. The model logic dis- 
counts the "as is" future outlay and distributes it over the period extend- 
ing from the present to the end of the replacement life. There is no effect 
on the project formuation calculations. 

To implement the required logic the countermeasures that are sur- 
face courses are given the smallest subscripts (after subscript 1). If the 
largest subscript for surface courses is KSM, this value will be used in the 
tests to determine if capital costs in the base condition should be included, 
The test is part of subroutine SOC. 



I. Right-of-Way Costs 

Only a few countermeasures may involve ROW (Right -of -Way) costs. 
Examples are: added turn lanes at intersections or driveways, added con- 
tinuous turn lanes in retail commercial areas, and reconstructed horizontal 
curves. Countermeasures which involve ROW costs require additional input 
from the program user and use of additional logic in the computer program. 

Each countermeasure that may require ROW costs has two subscripts 
associated with it. The smallest of the two subscripts is employed to iden- 
tify the countermeasure and the costs, lives, etc. associated with the non- 
ROW aspects of the countermeasure. The larger subscript for countermeasure 
KM is equal to KM 4- K2, ana is used for the ROW costs, life or amortization 
period, and final capital worth supplied by the program user. The data items 
required are: 

LIFC(KM + K2) , the ROW life or amortization period; 

SCAPC(KM + K2), the capital cost per unit of ROW; 

UN(KM + K2) , the number of ROW units required; and 

FCW(KM + K2), the final capital worth per ROW unit after 
LIFC(KM + K2) years. 

The logic in subroutine EACC calculates the equivalent uniform annual capital 
costs for (KM) and (KM + K2) separately and then combines them under sub- 
script KM for the total equivalent uniform annual capital cost EUACC(KM). 
The capital outlay is also combined under KM as C0L(KM) . The logic in sub- 
routine EACC also requires that: 

KM2 = Smallest subscript of countermeasures which may require ROW. 



23 



KM3 = The next subscript value above the range for countermeasures 
which may require ROW. 

The above logic provides an equitable inclusion of costs for ROW 
that usually has a much longer life than other countermeasure capital items. 
The logic can also be employed for equitable costing in circumstances such 
as described in the following paragraphs. 

Countermeasures that require ROW may be considered for facilities 
that are scheduled for rebuilding in a future year. However, the counter- 
measure may require that part of the future ROW be acquired in advance of the 
time it would be needed for overall rebuilding. In this case, the input data 
should include the total acquisition costs per unit of needed ROW as SCAPC 
(KM 4- K2). However, the life LAF(KM + K2) should be supplied as the time 
(years) until normal acquisition, and final capital worth FCW(KM + K2) 
should be input equal to SCAPC (KM + K2) . As a result the countermeasure 
will be charged a cost equal to the interest for the advanced capital out- 
lay, only. 

In this circumstance the countermeasure construction may be com- 
patible with the future rebuilding plans, so that a part of the counter- 
measure construction costs will be recovered during scheduled rebuilding. 
Input to the computer program, FCW(KM), can specify a final capital worth 
after a life LAF(KM) (also input to the program) that reflects the amount 
recovered and time until recovery. 

In case ROW is available, no charge for ROW costs should be made 
against the countermeasure. That is, SCAPC (KM + K2) = 0. (CAPC(KM + K2) 
is always left equal to zero.) Likewise, if ROW is obtained for future re- 
building on a schedule that makes it available earlier for the countermea- 
sure, the capital costs for ROW should be zero. 



J. Weight Factors for Certain Costs 

Two types of cost and benefit data have strong influences on econ- 
omic analyses of highways and traffic, yet are very controversial. They are 
the costs of injury and fatal accidents, and the value of time. The program 
employs standard values and costs in the data files, but also gives the user 
the option of assigning separate weight factors for each of the above in 
input. The weight factors can thus be used in sensitivity tests or to apply 
extra emphasis to the accident reduction aspects of countermeasures. The 
standard cost values are described more fully in Sections K and L. 



24 



The weight factor symbols are: FPD( ) for property damage only, 
FIA( ) for injury accident, FFA( ) for fatal accident, and FUTC( ) for value 
of highway users' time. The default values (subscript 1) are all 1.0 and 
are set in subroutine PREPI. These values may be superceded by input read 
in REED or the range of subscripts MVAR can be increased to correspond to 
additional sets of factors supplied in input. 



K. Accident Severities a nd Costs 

Accident severities are classified as property damage only, injury, 
and fatal. The user of the computerized model is given the option of sup- 
plying the baseline year (year before implementation of countermeasure) ac- 
cidents by severity or total only. If the baseline year accidents are pro- 
vided by severity, that distribution is employed for the precountermeasure 
condition. If only the total is supplied, default distributions are supplied 
by the model. The default distributions of severities are distinct for area 
type-highway type combinations. The area types are rural and urban; the 
highway types are two-lane uncontrolled access, multilane uncontrolled access, 
and multilane controlled access. The default distributions currently in the 
model are based on data from the states of California, Michigan, and Wash- 
ington. The numerics are presented in Appendix C. 

The cost per accident in each of the severity classes is formed 
as the product of the cost per unit involved and the average number of units 
per accident in the severity class. For property-damage-only accidents, 
the unit is a vehicle. For injury accidents, the unit is an injured person; 
in fatal accidents, the unit is a fatally- injured person. In the injury 
and fatal classes the property damage costs are included in the costs given. 

The assembly of standard accident costs for each severity is per- 
formed outside the model as the products indicated above. The values ini- 
tially supplied with the model are presented in Appendix C. The standard 
costs per accident by severity are part of the data files accessed by the 
computer program. If the model user specifies weight factors for accident 
costs (other than the 1.0 defalut values), those factors are applied in the 
computer program. 

When the model treats accident reductions, the injury and fatal 
severities are combined. This approach is consistent with the accident re- 
duction data and the small sample problems that attend fatal accident re- 
ductions. It should, however, be recognized that the initial (precounter- 
measure) distribution employs injury and fatal severities separately so 
that accident costs in the baseline and in the countermeasure conditions 
correctly reflect the accident costs at the site analyzed. 



25 



L. User Costs 

The user costs incorporated in the model are those arising from 
construction associated with the countermeasures. * The costs are due to 
increased delay (vehicle-hours/year) and excess fuel consumed (gallons/year) 
in years when construction occurs. The costs are incurred in the baseline 
year (prior to countermeasure implementation) and periodically in future 
years if the countermeasure is replaced in the period analyzed. The cost 
per vehicle-hour and per gallon of fuel is part of the data file, so that 
current values will be available from updated files. 

An analysis was performed to evaluate the added delays and in- 
creased fuel consumption associated with the countermeasures. The results 
are incorporated in the benefit-cost model in convenient analytical forms. 
The delays considered are those due to queuing and to depressed speeds at 
the construction zone. The added fuel consumptions considered are due to 
idling in queues, speed change cycles, and depressed speeds. The delays and 
the fuel consumption depend on the area type, the normal highway configura- 
tion, the construction zone configuration, the zone length, the ADT, the 
daily schedule for construction zone configuration, and the number of calen- 
dar days required. 

The basis for delay and fuel consumption calculations is presented 
in Appendix D together with available numerical results. 



M. Maintenance and Operating Expenses 

The annual maintenance and operating costs in the model are the 
algebraic sum of two components. The first component is the normal average 
cost per mile AGMA0(IATYP, IHTYP) , which is dependent on area type and high- 
way, type. The second component is the change or increment in maintenance 
and operating costs arising from the countermeasure. 

The individual countermeasures influence maintenance and operating 
expenses in one of two ways. Those countermeasures that add equipment 
(signing, markers, lights) or new pavement (turning lanes, climbing lanes, 
widened traveled way) or other structures increase maintenance and operating 
expenses. On the other hand, those countermeasures that renew, replace or 
protect the existing surface course, change the sequence of yearly expenses 
and have a tendency to reduce those expenses in the near future. 



User costs applicable to specific area and highway types could be added 
to the model, and would make it useful for benefit-cost calculations 
applicable to reconstruction that changes highway type. 



26 



It was not possible to locate representative data that quantify 
the relationships described above. Because of the current lack of well- 
defined data, the model is configured to facilitate sensitivity tests using 
appropriate analytical forms. 

The count ermeasures that add equipment, pavement, or structure 
will clearly add maintenance and possibly operating costs associated with 
the quantity of the count ermeasure employed. The model employs the average 
annual maintenance and operating cost per unit of count ermeasure, CMA0(KM), 
provided by the support system data files unless the user supplies an over- 
riding value, SCMA0(KM). Although the yearly costs for the maintenance and 
operation of these countermeasures may exhibit changes with the years of 
service, the year-to-year variation is not included in the model. Thus, 
the model uses CMA0(KM) or SCMA0(KM) each year as the second component of 
the annual maintenance and operating expenses. Examples of such expenses 
would be sign replacement and cleaning, added winter maintenance for the 
new pavement, etc. 

Countermeasures that consist of surface courses, surface treatments 
and surface seals influence the subsequent sequence of yearly maintenance 
expenses. The maintenance costs for the first year following resurfacing 
can be reduced below the annual average, and they can then increase linearly 
with time to a maximum where they remain constant. The second component for 
these countermeasures in the model is the lesser of 

CMA0(KM) + JY * CCMA0(KM) 
or 

CMA0M(KM) , 

where CMA0(KM) will usually be negative and CCMA0(KM) , the rate of change, 
is positive ana is multiplied by the number of years, JY , since emplace- 
ment. CMA0M(KM) is used to set a maximum for the second component of main- 
tenance and operating cost. Examples of maintenance and operating expenses 
for these countermeasures are patching and sealing. 



N. Traffic Volumes 

The measure of traffic volume used by the model is the Average 
Daily Traffic (ADT) . The model considers three types of sites: inter- 
section sites, non- intersection sites (see Section VI. B) and highway sections. 
The model has the capability to handle traffic volumes for either one or 
two facilities at each site. At an intersection site, one of the intersec- 
ting roadways is designated as the major facility and the other is designated 

27 



as the secondary facility. In this case, the user must supply traffic volume 
estimates for both facilities. For highway sections and non- intersection 
sites, traffic volumes are needed for only one facility—the major facility. 

The model requires an estimate of ADT for each facility in each 
year of the analysis period. The user can specify these traffic volumes 
by either of two alternative methods: (1) by specifying the ADT for the 
year when implementation of the countermeasure is planned and the rate of 
ADT growth, or (2) by directly identifying the ADT year-by-year for the en- 
tire analysis period. 

The first method uses the following functional relationship to 
project the growth of traffic volumes: 

ADTM(m) = TIM + (TIM) (~p) (m) + TIM|7™££ + l\ m -1 

where ADTM(m) = ADT of major facility in year m, 

TIM = ADT of major facility during year when countermeasure 
is implemented, 

TMGL = Percent growth rate for linear ADT growth, and 

TMGC = Percent growth rate for compounded ADT growth. 

ADT growth for the secondary facility is treated in a similar fashion. 

The base for ADT growth, TIM , is the estimated ADT for the 
year when the countermeasure will be implemented. The user can choose 
either linear or compound growth for ADT by the selection of values for 
TMGC and TMGL . For example, if TMGL = 5% and TMGC = 0% , then ADT 
will have a linear growth at a rate of 5% per year. However, if TMGL = 0% 
and TMGC = 5% , ADT growth will be at the rate of 5% per year, compounded. 

Alternately, the user can specify year-by-year ADT values for 
both the major and secondary facilities. This option is useful when the 
ADT growth pattern cannot be specified by a simple percentage rate. For 
example, an abrupt decrease in traffic volume on a facility, caused by the 
opening of a parallel facility during the analysis period, cannot be described 
by a simple function. In such cases, the user can provide the best estimate 
of ADT for each year of the analysis period. 

The model uses the same projected traffic volume data in the anal- 
ysis of all countermeasures. It assumes that none of the countermeasures 
has an effect on the traffic volume at the site during the analysis period. 

28 






0. Skid Numbers 

An in-depth examination was made of the factors that determine 
skid numbers and of the associated field and laboratory findings. It is 
clear that skid numbers depend on the aggregate mineralogy, initial shape, 
size grading, the binder or cement characteristics, the emplacement prac- 
tices, and various wear and weathering processes after emplacement. These 
factors are discussed in Appendix B. It is concluded that it is currently 
impractical to establish numerically defined values for skid numbers that 
will be appropriate for widespread application to any one of several types 
of surface courses. Instead, it is clear that even subtle variations in 
mineralogy, binders and emplacement practices, and the regional variations 
in wear and weathering combine to make skid number prediction a strictly 
local necessity. 

As a result of the above findings, the computerized model contains 
a simple analytical form for skid number as a function of accumulated ve- 
hicle passages. The form is known to be applicable to pavements with pol- 
ishing aggregate and it appears to be suitable for nonpolishing aggregate 
as well. 

Within the computerized model the skid number, SN , is calculated 
as 

SN = SD0 + CS * AL0G(AMAX1(1.O, CT/ 100000.)) 

where SD0 = Initial skid number, 

CS = A rate of change with the (natural) log of vehicle passages, 

CT - Accumulated vehicle passes since surface emplacement, 

and the AMAX1 function indicates that 1.0 is used in place of CT/ 100000. 
when CT/ 10000. is less than 1. 

In addtion, bounds can be set on the final value of skid number, 
SDF (when CT is large). If CS is negative (i.e., a polishing aggre- 
gate surface), SDF is used as a lower bound for SN. If CS is positive 
(i.e., a true nonpolishing aggregate surface), SDF is taken as an upper 
bound for SN . 

Within the computerized model the coefficients and limit values are 
carried as subscripted symbols SD0R(KM), CSR(KM), and SDFR(KM), where the 
subscript, KM, identifies the counterseasure with those coefficient values. 



29 



The skid number calculations for a counterrneasure are set up in 
subroutine SKIDI and are evaluated for each year analyzed in subroutine 
SKIDC. Routine SKIDC also keeps track of pavement surface life; and, if the 
period of analysis extends past the end of surface life, the pavement is re- 
newed (analytically) and accumulated traffic passages begin again at zero. 
For the base case, i.e., the "as is" condition, logic will start CT at a 
nonzero value for the zeroth year if the pavement has been used and there is 
no prior decision to alter it. 

The skid number is conventionally measured directly with a skid 
trailer. However, a relationship developed by Penn State University pro- 
vides estimates of skid number from separate measures associated with surface 
microtexture and macrotexture. The relationship is: 

-r0.041V/(MD)°* 47 ] 
SN V = (-31.0 + 1.38 BPN)e L V ' J 



where SNy = Skid number at speed V(mph), 

BPN = British Portable Number, and 

MD = Mean texture depth (milli-in.) determined by the sand patch 
method. 

The model uses skid number at a speed of 40 mph, so the appropriate 
form is obtained by substituting 40 mph into the previous equation: 

SN = (-31.0 +1.38 3 PN)e- [U64/(MD)0 ' 47 J 
4U 

This equation is employed in the model for two purposes. First, the initial 
skid number of a surface course can be specified through BPN and MD. In the 
computer program the symbol names are BPNR( ) and AMDR( ) where the subscript 
( ) identifies the counterrneasure. These values are read in subroutine REED. 
When they are supplied, the skid number calculated from BPNR( ) and AMDR( ) 
will be used in place of SD0R( ). 

The Penn State equation is used in the second application to cal- 
culate the skid number for the "as is" pavement. The program user supplies 
the data with symbol names BPNY0 and AMDY0. These data may be supplied by 
the user in place of SNY0. However, if SNY0 is supplied as input it will 
be used. 

In either case (new or existing pavement surface) the skid number 
is subsequent years is calculated using the first equation in this section 
where skid number is a function of accumulated vehicle passes, CT. 

30 



VI. ACCIDENT RATES AND COUNTERMEASURE EFFECTS 

The computerized benefit-cost model uses the results from Phase I 
analyses of the relationships between skid number and accidents. It meshes 
these with previously published data on the accident reductions achieved 
through geometric and traffic control countermeasures. This combination 
gives the model the capability to evaluate the entire range of wet-pavement 
accident countermeasure types. The analysis of the combined forms also 
indicates that the effectiveness of geometric and control countermeasures 
is not independent of skid number. 

This section of the report presents the results from Phase I 
analyses that are directly applied in the model. The relationship of these 
results to countermeasure effectiveness is shown. The relations employed 
in the model are derived in brief and the resulting forms are presented. 
The incorporation of geometric and control countermeasures is described. 
The influence of ADT on accidents is presented together with the forms 
employed in the model. Finally, a description is provided of the model's 
overall handling of accident rate calculations. 



A. Results From Analyses of Skid Number and Accident Rates 

Three major findings are incorporated in the model. First, there 
is the general finding that the wet-pavement accident rate, r w , is corre- 
lated with skid number, S , in the anticipated way. That is, the wet- 
pavement accident rate is decreased for higher skid numbers. The exact 
relationships are dependent on the area type and highway type, and these 
relationships are well defined by available data only for rural areas, 
where sample sizes are largest. 

The second major finding is that the relationship between the 
wet-pavement accident rate, r w , and skid number, S , is strongly de- 
pendent on the dry-pavement accident rate, r^ . This finding is illus- 
trated in Figure 4 where or w , the rate of change of the wet-pavement 

Ts~ 

accident rate with skid number, is plotted against the dry-pavement acci- 
dent rate for all rural highway types. The magnitude of or w is indicative 

of the relative sensitivity of wet-pavement accident rate to skid number 
(i.e., the slope of the wet-pavement accident rate- skid number relationship) 
This sensitivity, which is for the most part in accord with expectations, 
is now discussed. 

In Figure 4, and in the underlying analyses, the dry-pavement 
accident rate is used as a proxy variable. It is reasoned that where dry- 
pavement accident rates are relatively low there will be a less- than-average 



31 



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-0.10 ~ 



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■0.06 ™ 



-0 04 



■0.02 ~ 



• Two-Lane, Two-Way (86 Sections Per Point) 

O Multi-Lane, Uncontrolled Access (16 Sections Per Point) 

A Muti-Lane, Controlled Access (16 Sections Per Point) 




@ 



0.02 



Note: Circled points are those retained to provide 
the best linear regression 



1 2 3 4 5 6 

Dry-Pavement Accidents Per Million Vehicle Miles 

Figure 4 - Rate of Change of Wet-Pavement Accident Rate with Skid 
Number As a Function of Dry-Pavement Accident Rate 
for Rural Highways 



32 



demand for skid resistance to avoid accidents on wet pavements. This should 
be associated with a small sensitivity. Likewise, high dry-pavement accident 
rates are an indication that there will be sizeable demands for skid resis- 
tance to avoid accidents on wet pavements. In these cases, the sensitivity 
should be large in magnitude. The plotted points in Figure 4 generally 
conform to the preceding concepts. In fact, when the dry-pavement accident 
rate is used as a factor the sensitivity of wet-pavement accident rate to 
skid number is explained as well as by any other choice of factors. 

The relationship between §r w and r, is approximated in the 

model by three line segments as shown in Figure 4. At low dry-pavement acci- 
dent rates, r^ < 1.08 accidents/million vehicle miles (MVM) , the sensitivity, 
3r w , is zero. In the range, 1.08 ^ r^ < 3.02, the magnitude* of the 

sensitivity increases linearly, and for r-. ^ 3.02 the sensitivity remains 
constant.''"'' The correlation coefficient of the linear regression line for 
the range 1.08 r^ 3.02 in Figure 4 is 0.78. This relatively high cor- 
relation coefficient should not be misinterpreted. The slopes used in this 
regression analysis are themselves the result of regression analyses that 
range in correlation coefficient from 0.02 to 0.33. Therefore, the reli- 
ability of Figure 4 to predict the rate of change of wet pavement accident 
rate with skid number for any particular section is limited. However, Figure 
4 is the most reliable representation of the important sensitivity of the 
slope of the wet-pavement accident rate- skid number relationship to dry- 
pavement accident rate identified in Phase I. A description of the develop- 
ment of this relationship is found in Volume I. 

In the model, it is assumed that the wet-pavement and dry-pavement 
accident rates prior to application of a countermeasure are known. These 
initial estimates will be based on historical experience at the site or, in 
the case of new or rebuilt facilities, on professional judgement considering 
similar facilities. Then, if a change in skid number is contemplated as a 
remedial measure, the rate of change of the wet-pavement accident rate with 
skid number can be estimated. 



* All non-zero values of §r w are negative. This is expected, indicating 

w 

that wet-pavement accident rates diminish as the skid number increases. 
** The leveling off of 5r w at large r^ was not anticipated. There are 

several potential explanations for this, although none of them have 
been explored. One possibility involves the kind of rate averaging 
implicit in using data from sections more than 1 mile long. Another 
possibility is that on sections with very high dry-pavement accident 
rates, many of the accidents may arise in situations where moderate 
changes in skid resistance has little effect. 



33 



Although the data on urban sections were not extensive enough to 
establish separate relationships, statistical tests indicate that the 
sensitivities for urban areas are likely to be different than the rural 
values. However, the general character of the relationships should be 
similar. Lacking definitive data, the rural relationships are applied in 
the model to urban sites as well as best available estimates. 

The third major finding incoporated in the model is the set of re- 
gression results that relate dry-pavement and wet-pavement accident rates. 
Regression equations were obtained separately for each of six combination 
of area type and highway type. Statistical tests indicated that the inter- 
cepts (r w at r^ = 0) are indistinguishable, but that there are two different 
slopes (dr w /dr^) as indicated in Table 1 and Figure 5. Therefore, two dis- 
tinct relationships between wet- and dry-pavement accident rates are employed 
in the model. No explicitly determined correlation coefficient was deter- 
mined for these relationships because of the manner in which the analysis 
was performed. However, the overall goodness of fit can be judged from the 
correlation coefficients for the six regression equations used to develop 
the two relationships. The correlation coefficients for these six range 
from 0.38 to 0.69. As would be expected, these results indicate that wet- 
pavement accident rates are generally higher than dry-pavement rates. It 
is note able, however, that on rural highways and on urban, two- lane high- 
ways, the wet-accident rate does not increase quite as fast as the dry- 
accident rate. 

The relations between wet-pavement and dry-pavement accident rates 
and the sensitivity of wet-pavement accident rates to skid number were com- 
bined in the computerized model. The final forms used are presented in 
the next section. 



B. Basic Equations Depicting Skid Number -Accident Rate Relationships 

The incorporation of the skid number-accident rate relationships 
employs several simple concepts. First, the overall accident rate on a 
facility is approximated as a linear combination of the rates under wet- 
and dry-pavement conditions: 

r = f w r w + f d r d ' 

where r = Overall accidents per MVM 

f w = Fraction of time pavement is wet, 

r w = Accidents per MVM under wet-pavement conditions, 

f<j = Fraction of time pavement is dry, and 

rj = Accidents per MVM under dry-pavement conditions. 

Second, the wet-pavement accident rate is expanded as the sum of a part 
correlated with the dry-pavement accident rate and a part containing the 
skid number sensitivity: 

34 



r w = b o 



+ b l r d 



+ |r„ (S - S) 



'W 



9^> 



where b and b^ are coefficients 
40 mph (64 km/hr); and S 
for which r w = b Q + b^r^ 
Table 2 the values for S*. 



S is the skid number measured at 
is the average skid number (40 mph or 64 km/hr) 
Table 1 gives the coefficient values, and 



TABLE 1 



REGRESSION COEFFICIENTS, b Q and b-j^ 



Area Highway 
Typea/ 



Common 

Intercept (b ) 
o 



Common 
Slope (b ) 



R2LUA 
RMLUA 
RMLCA 
U2LUA 



0.8066 
0.8066 
0.8066 
0.8066 



0.8281 
0.8281 
0.8281 
0.8281 



UMLUA 
UMLCA 



0.8066 
0.8066 



1.4873 
1.4873 



i/ R2LUA = Rural, two-lane, uncontrolled access. 

RMLUA = Rural, multilane, uncontrolled access, 

RMLCA = Rural, multilane, controlled access. 

U2LUA = Urban, two-lane, uncontrolled access. 

UMLUA = Urban, multilane, uncontrolled access 

UMLCA = Urban, multilane, controlled access. 



TABLE 2 



AVERAGE SKID NUMBERS AT 40 MPH (64 KM/HR) 







Ave 


rage Skid Number 


Area, Highway 




at 40 mph 


Type 






(64 km/hr) 


R2LUA 






47.97 


RMLUA 






45.50 


RMLCA 






44.59 


All Rural 


(weighted) 


47.17 


U2LUA 






41.04 


UMLUA 






38.90 


UMLCA 






39.27 


All Urban 


(weighted) 


39.74 



Sample 
Size 

518 

97 

97 
712 

32 
34 
28 
94 



Unweighted 
Averages Employed 
in Model 



46.0 



39.7 



35 



16 r- 



14 



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u 

IE 

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c 
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0) 

E 
o 

> 

D 

a, 
t_ 

% 



All Urban 
Multi Lane 
Highways 




All Rural Highways and 
Urban Two- Lane Highways 



2 4 6 8 10 

Dry-Pavement Accidents Per Million Vehicle-Miles 

Figure 5 - Relation Between Dry-Pavement and Wet-Pavement Accident Rat 

36 



es 



In addition, in agreement with Figure 4, a three segment repre- 
sentation for ^ r is employed where each segment has the form 

B£w = a Q + a x r d 

where the coefficients, a n and a-i , given in Table 3, depend on the dry 
pavement accident rate. However, as will be shown subsequently, it is 
practical to select the appropriate a and a^ on the basis of overall 
accident rate. 



TABLE 3 

REGRESSION COEFFICIENTS a Q AND a]-' 

Range of r d a a^ 

£ r d £ 1.082 

1.082 < r d < 3.02 0.04615 -0.04264 

3.02 £ r d -0.0825 



a/ The coefficients are based on all rural highway types combined, but 
are used for urban highways as well, because of a lack of more de- 
finitive data (see text, Section VI. a). 



C. Graphical Visualization of Countermeasure Effects 

Figures 6 and 7 illustrate overall accident rates as functions 
of skid number and dry-pavement accident rate for climates that produce 
wet highways 10% and 30% of the time. These figures were plotted from the 
equations in the preceding section. 

The effects of countermeasures can be visualized on either figure. 
When a geometric or traffic control countermeasure is applied, the improve- 
ment is reflected by a displacement along the line of constant skid number 
to a lower accident rate. When the skid number is increased, the improve- 
ment is reflected by a vertical displacement to lower total accident rate 
(presumably, at a constant dry-pavement accident rate) . Some countermeasures 
may involve both effects. For instance, pavement grooving appears to in- 
fluence both wet- and dry-pavement accident rates at some sites. The grooves 
may act to alert drivers under all conditions. 



37 



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38 



Figure 6 illustrates the small effect of skid number on overall 
accident rates when the pavement is wet only 10% of the time. Similarly, 
on sections with low dry-pavement accident rates, the data collected in 
this project indicates there is no sensitivity to skid number. Therefore, 
(quite logically) skid number improvements are most likely to be cost bene- 
ficial on sections with relatively high accident rates and where pavements 
are wet a large fraction of the time. 

The figures suggest that maximum benefits accrue at very high 
skid numbers (60) . These benefits should be viewed with reservation. 
First, a skid number of 60 is close to the maximum attainable with special 
surface courses incorporating either rare or manufactured aggregate. Second, 
although the Br /rS is constant according to the data analyses, the confi- 
dence interval is wide at extreme skid numbers . 

There is another aspect that deserves attention. At high acci- 
dent rates the overall accident rate is less than the dry-pavement rate for 
large skid numbers. This situation arises because the predictor equations 
yield wet-pavement accident rates less than dry-pavement rates when there 
are large skid numbers in conjunction with large dry-pavement accident rates. 
It is difficult to determine if this phenomenon is real. Certainly there 
are numerous facets of driving other than skid resistance that deteriorate 
in wet weather. The visual aspects are most obvious —more obscuration, 
reduced visual range, reduced contrast during daytime, and increased glare 
at night. Factors that might decrease wet-weather accidents are less obvious. 
Field measurements indicate that average speeds are reduced very little in 
' wet weather. However, it may be more important to know if the speed dis- 
tribution is affected, with reductions in the extremely high speeds. 
For example, previous analyses of speeds in horizontal curves^J^.' suggest that 
the highest speeds then must be reduced on wet pavements to avoid frequent 
skidding. 

Available information is not sufficient to evaluate the likelihood 
that wet-pavement accident rates may be less than dry-pavement rates under 
some conditions. In any event, the benefits indicated for very high skid 
numbers may be overestimated. 



D. Forms Employed In the Model 

The equations presented in Section B can be combined to form the 
basic equation: 

r = f f".b rt + b 1 r J + (a + a,r,) (S - S)l + f ,r . 
wLo Id o ld /v y J d (j 

The change in overall accident rate with skid number is given by 
the partial derivative: 



39 



Br = (a + ai r d )f w . 
3S 

Thus, an incremental change in skid number (AS) will produce an incremental 
change in overall accident rate (Ar) of 

Ar = -^AS 

= (a + a 1 r,)(AS)f . 
o 1 d M w 

Using the basic equation and the forms illustrated in Figure 4, 
the expression, _Sr , can be obtained as 

as 

Sr = 

ds 

for r £ v 1 = f w [b Q + 1.082 (b ± - 1)] + 1.082. 
If r > r x , 

Sr = -0.0825 f 



ss 



w 



or 



f w (r " r l>V { f w [ b l + a l < S o - ^ + (1 - f v>( . 

whichever is algebraically larger. S is the skid number applicable when r 
was established as the accident rate, and normally is the skid number prior 
to a change due to countermeasure implementation or pavement use. The 
coefficients for these equations have values that depend only on area type 
and highway type. They are summarized in Table 4. 

These equations together with the coefficients in Table 4 are 
employed in the model to calculate 5 r/SS and then adjust the accident 
rate for changes in skid number. The equations are in subroutine SNADJ 
where or/oS has the symbol name, DRDS , the incremental change in skid 
number is SN-SN0LD , and overall accident rate has the symbol name ARC. 



40 







TABLE 4 








SUMMARY OF COEFFICIENTS FOR EQUATIONS 








EMPLOYED 


IN MODEL 






Area Highway 
Type^/ 


S 
46.0 


-0.64264 


bo 
0.8066 


0. 


5l 


R2LUA 




8281 


RMLUA 




46.0 


-0.64264 


0.8066 


0. 


,8281 


RMLCA 




46.0 


-0.64264 


0.8066 


0. 


8281 


U2LUA 




39.7 


-0.64264 


0.8066 


0. 


8281 


UMLUA 




39.7 


-0.64264 


0.8066 


1. 


,4873 


UMLCA 




39.7 
, two- 


-0.64264 0.8066 1. 
lane, uncontrolled access. 


4873 


a/ R2LUA = 


Rura 1 . 




RMLUA - 


Rural. 


, multilane, uncontrolled access 




RMLCA = 


Rural. 


, mult 


ilane, controlled access. 






U2LUA = 


Urban, 


, two- 


lane, uncontrolled access. 




UMLUA = 


Urban. 


, mult 


ilane, uncontrolled access. 




UMLCA = 


Urban. 


, mult 


ilane, controlled access. 







41 



The Phase I analyses indicate that wet pavements and skid numbers 
can also impact the effectiveness of geometric and traffic control counter- 
measures. This is apparent from Figures 6 and 7, where such countermeasures 
can be thought of as acting directly on the dry-pavement accident rate. 
When the dry-pavement accident rate is reduced by a fixed percentage, the 
reduction in total accidents is sensitive to the fraction of time pavements 
are wet, and to the skid number if the accident rate is in the middle range 
where the lines fan out. In this range a low skid number should cause the 
geometric or control countermeasures to be relatively more effective. 

The skid numbers and the fractions of time that pavements were 
wet during countermeasure evaluations will affect the results of those 
evaluations. The basic equation for overall accident rate can be applied 
to determine a factor to correct the evaluated percent reduction, P , to 
the percent, p , that can be expected in application: 



p - { f w [bi + &1 (S - S)] + f d | P 



where F and F_, = Fractions of time pavements in the countermeasure 

evaluation region were wet and dry, 

and the other symbols retain their previous meanings. The variable, a-]_ , 
depends upon the dry-pavement accident rate at the application site, so 
must be approximated using the initial overall accident rate at the appli- 
cation site. The coefficient of P is the correction factor; it has the 
symbol name GC0R and is calculated in subroutine C0RRT. 

Spot-site accident rates are also treated by the model. However, 
the data and analyses from Phase I deal with accident rates (accidents/ 
MVM) on sections of highway, whereas at spot sites it is conventional to 
use accidents/MV. In the model, it is postulated that the spots in question 
have higher than average accident rates, so that the sensitivity to skid 
number should be equal to or greater than the sensitivity in highway sections, 
Although the leveling off of that sensitivity at very high accident rates on 
sections raises questions about the postulate, the postulate of similarity 
between spots and sections still provides the only estimate and it is used. 

Analytically in the model it is assumed that each spot site 
analyzed has an initial accident rate that is equivalent to the section 
rate at the upper end of the middle range. (This is at the upper end of 
the fan of lines on Figures 6 and 7.) Using this assumption the precounter 
measure (year zero) accident numbers are used to calculate a pseudo length 
for the spot; it is given the symbol name SLGTH. This calculation is in 
subroutine C0RRT. The modifications and adjustments to accident rate are 
then handled by the same logic employed for sections. 



42 



E. Macrotexture - Accident Rate Relations 

Macrotexture influences wet-pavement accident rates through its 
effect on skid number. The Penn State equation, described in V-0, which 
quantifies the effect is employed in the model. Hoi^ever, macrotexture is 
also thought to influence through its effect on the potential for hydro- 
planing. Analyses to date of available data have not been able to quantify 
this effect. As described in Volume I of this report, it is possible that 
the analyses of wet-pavement accident rate-macrotexture correlation have 
been diluted by variances that could be reduced. The reduction of unneces- 
sary variance might be accomplished by using weight factors based on the 
established correlations with dry pavement accident rate. If additional 
relationships between macrotexture and wet-pavement accident rates become 
available they should be incorporated in the model. The following para- 
graphs describe the routines that may be affected. 

In system files , it will be necessary to provide subscripted 
symbols for the pertinent measure of initial macrotexture for each counter- 
measure involving the pavement surface. If mean texture depth is a satis- 
factory measure the subscripted variable AMDR( ) will suffice. 

In input routines , provision will be required for a macrotexture 
measure for the existing pavement surface. If mean depth is used AMDY0 will 
suffice. 

In all the following routines , provisions should be made to use 
suitable average values if the macrotexture data is not supplied. 

In subroutine C0RRT , it may be necessary to adjust the benefits 
expected from nonsurface countermeasures for the effects of zero-year 
macrotexture. 

In subroutine SKIDI , set parameter values for calculation of macro- 
textures during the period of analysis. 

In subroutine SKIDC , provide for updating macrotexture for each 
year of the analysis period, or for reinstating macrotexture to new pave- 
ment value in any year when the surface is replaced. 

In subroutine SNADJ , provide for change in wet-pavement accident 
rate due to change in macrotexture. 



43 



F. Accident Rates Associated With Geometric and 
Traffic Control Countermeasures 

One of the most useful features of the model is its ability to 
compare the effectiveness of geometric and traffic control countermeasures 
with the effectiveness of countermeasures that involve modification of pave- 
ment surface characteristics. Although the state-of-the-art of accident 
reduction effectiveness estimates for geometric and traffic control counter- 
measures is limited, those estimates that are available from previous re- 
search have been incorporated in the model. The user has the option of 
replacing the effectiveness estimates taken from the literature with esti- 
mates more appropriate to a particular region or a particular site. In 
addition, countermeasures other than those explicitly incorporated in the 
model can be evaluated using user-supplied effectiveness estimates. 

Table 5 presents the accident reduction effectiveness estimates 
from the literature that are incorporated in the model. These estimates 
are expressed as percent accident reductions which are applied to the acci- 
dent experience for the site under analysis. The effectiveness estimates 
found in Table 5 were obtained from the User's Manual in NCHRP Report 162. zJL' 
The estimates in that manual were obtained from a study conducted in 1966 
by Roy Jorgensen and AssociatesiLzL' and from estimates supplied directly by 
the States of California and Mississippi. The estimates in Table 5 are the 
most reliable that are currently available. However, as more reliable esti- 
mates become available in the future, the estimates currently incorporated 
in the model can be replaced. 

Table 5 contains the following information for each geometric 
and traffic control countermeasure incorporated in the model: 

Site type for which countermeasure is appropriate 

Indication of whether or not the countermeasure may require 
acquisition of additional right-of-way 

Number used to identify the countermeasure in the model 

Countermeasure name 

Area type for which accident reduction effectiveness estimates 
are appropriate 

Highway type for which accident reduction effectiveness esti- 
mates are appropriate 

Fraction of time with wet pavement for which accident reduction 
effectiveness estimates are appropriate 

44 



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Percent accident reduction effectiveness for all accidents 
or for accidents broken down by severity, accident type, 
pavement condition or light condition* 

The accident reduction effectiveness of each counterraeasure specified by 
the user is evaluated in Subroutine CREDIT, presented in Appendix E. The 
purpose of this subroutine is to determine the total of fatal-plus-injury 
accidents and the number of property-damage-only accidents that remain in 
the year after the countermeasure is implemented. The following discussion 
describes the use in this subroutine of each type of information described 
in Table 5. 

1. Selection of countermeasures for analysis : The user may select 
one or more countermeasures that are appropriate for a given site by speci- 
fying the countermeasure numbers given in Table 5. The user must exercise 
judgment in selecting the countermeasures to be analyzed. The burden is 
on the user to decide whether each potential countermeasure is warranted 
and feasible. 

Many of the countermeasures in Table 5 are applicable to all high- 
way types and area types, but the estimates for some countermeasures are 
only applicable to certain specified area types or highway types. For ex- 
ample, the accident reduction effectiveness estimate for installation or 
improvement of edge markings, the first countermeasure shown in Table 5, 
is only applicable to rural, two-lane highways. If the user specifies this 
countermeasure for use with any other highway type or area type, an appro- 
priate message will be printed to warn the user. However, since appropriate 
effectiveness estimates for other highway types and area types are often 
not available, this message does not prevent the program from performing 
the analysis of the countermeasure, because the estimate, however inappro- 
priate, may be the best available. 

Similarly, the program will check whether each countermeasure se- 
lected by the user is appropriate for the site being analyzed. Three typ^es 
of sites can be analyzed: (1) route sections, (2) non- intersect ion locations 
such as horizontal curves, grades, median openings, bridges, underpasses 
and railroad crossings, and (3) intersections. Each of the countermeasures 
in Table 5 are identified as appropriate to one of these three site types. 
The computer program will compare the actual site type with the site type 
appropriate for each countermeasure specified by the user. If any discrep- 
ancies are found a message will be printed to warn the user that the accident 
reduction effectiveness for the countermeasure he has specified may not be 
appropriate for the type of site under analysis. As with area type and 
highway type, the program will still complete the analysis of the counter- 
measure, even if an inappropriate site type is detected. 



There are no entries in the pavement condition columns and very few 

entries in the light condition columns in Table 5. However, these 

two breakdowns are included in the program logic so that the user 

can supply countermeasures not incorporated in the model that use 

these categories. 

52 



The countermeasures are also classified by whether or not they may 
require the acquisition of additional right-of-way. This classification is 
necessary because countermeasures that may require additional right-of-way 
employ different subscript ranges than countermeasures that do not require 
additional right-of-way, as explained in Section V.I. 

2. Countermeasure effectiveness estimates : The program will auto- 
matically use the effectiveness estimate contained in Table 5 for a counter- 
measure unless the user provides another estimate for one or more of the 
selected countermeasures. It is mandatory only that the user supply an 
effectiveness estimate for those countermeasures that are not included in 
Table 5 or that have no effectiveness estimate shown there. An error message 
will be printed if the user does not provide an effectiveness estimate for 
a countermeasure which requires one. The countermeasure in question will 
not be analyzed, but analysis of the remaining countermeasures will continue. 

As stated above, the accident reduction effectiveness estimates 
used by the model are expressed by one of five methods: 

Percent reduction by accident severity 
Percent reduction by accident type 
Percent reduction by pavement condition 
Percent reduction by light condition 
Percent reduction for all accidents 

Several methods have been used because the effectiveness estimates are pre- 
sented in the literature in a variety of forms. The five methods are listed 
above in priority order. The program will use the percent reduction by 
accident severity for a countermeasure if it is available in Table 5 for 
the countermeasure in question. If the percent reduction by accident seve- 
rity is not available, the program will use the percent reduction by acci- 
dent type, and so on. The percent reduction for all accidents will be used 
only if the percent reduction is not available for any of the four accident 
breakdowns. 

The countermeasure evaluations in the literature may have been 
performed under wet-pavement exposure and skid number conditions different 
from the analysis site. A correction factor is used in the modal to make 
the effectiveness estimates applicable to the wet-pavement exposure and lo- 
cal skid number of the analysis site. The percent reduction from Table 5 
is multiplied by the correction factor to obtain an adjusted percent reduc- 
tion. The correction factor, G , is given by: 

G = fy (bl + aj (SN40 o - SN40)) + f d 
_ ______ _ . 

where f w = Fraction of wet pavement time at site analyzed 

53 



f<j = Fraction of dry-pavement time at site analyzed = 1 - f w 
SN40 o = Skid number (at 40 mph) at site in zeroth year 



SN40 = Average skid number (at 40 mph) for area type and highway 
type 

F w = Fraction of wet-pavement time at sites where counter- 
measures were evaluated (given in Table 5) 

F d - 1 - F w 

b-j_ = Coefficient dependent on highway type and area type (given 
in Table 6) 

a]_ = Coefficient dependent on highway type, area type and over- 
all accident rate (given in Table 6) 

The model distinguishes only area type for estimating the average 
skid number at 40 mph, SN40 . The values assumed in the model for SN40 
are taken from Volume I of this report and are assumed to be 46.0 for rural 
highways and 39.7 for urban highways. These same values for SN40 are used 
regardless of the highway type and site type being analyzed. Note that the 
sensitivity of the correction factor to skid number is influenced by the 
coefficient a^ , which, in turn, is a function of highway type, area type 
and accident rate. Table 6 indicates that the correction factor is sensitive 
to skid number only within a limited range of accident rates. 

The typical fraction of wet-pavement exposure for the State of 
Mississippi was determined to be 0.20 from available weather records. There- 
fore, 0.20 was the value of F w used for countermeasures from the literature 
that were evaluated in Mississippi. The other countermeasures in the model 
were evaluated in the State of California, which has an extremely varied 
climate, or from data supplied by a number of states. For these counter- 
measures, a nationwide average value, 0.13, is used for F w . Table 5 
shows the value of F w used for each countermeasure. 

Table 7 illustrates the range of correction factors that can be 
expected for f w in the range 0.05 to 0.30 and SN40 o in the range 20 to 
60. 

3 . Calculation of accidents remaining after countermeasure imple- 
mentat ion: The user must provide the value of AALL , the total number of 
accidents expected to occur in the zeroth year if no countermeasure is 
implemented. If the only available effectiveness estimate for the counter- 
measure being evaluated is the percent of all accidents reduced, then the 
expected number of accidents remaining after implementation of the counter- 
measure is determined directly as: 



TABLE 6 



VALUES OF a x AND b x USED TO DETERMINE CORRECTION FACTOR, G 



Area Type 
and 
Highway Type 



Overall 

Accident Rate Range 

(accidents/MVM) 



a l 



R2LUA 
RMLUA 
RMLCA 
U2LUA 



to 1.75 
1.76 to (3.50 + 2.5 f„) 
> (3.50 +2.5 f w ) 



-0.04264 




UMLUA 
UMLCA 



to 2.00 
2.01 to (3.50 + 5.0 f w ) 
> (3.50 + 5.0 f w ) 





■0.04264 





Area Type 
and 
Highway Type 



R2LUA 
RMLUA 



I 

RMLCA ( 
U2LUA ) 



bl 



0.8281 



UMLUA 
UMLCA 



1.4873 



Key: 

f w = Fraction of time with wet pavement at site analyzed 

R2LUA = Rural, Two-Lane, Uncontrolled Access 

RMLUA = Rural, Multilane, Uncontrolled Access 

RMLCA = Rural, Multilane, Controlled Access 

U2LUA = Urban, Two-Lane, Uncontrolled Access 

UMLUA = Urban, Multilane, Uncontrolled Access 

UMLCA = Urban, Multilane, Controlled Access 



55 









TABLE 


7 












ILLUSTRATIVE 


VALUES OF THE 


CORRECTION FACTOR, 


G 


tion Fact 




Area Type 




Overall 






Correc 


or, G 


and 


fw 


Accident Rate Range 
(accident s/MVM) 


Si 


fl 




for SN40 o 




Highway Type 


20 


40 


60 


R2LUA 







to 1.75 


0.8281 





1.014 


1.014 


1.014 


RMLUA 


0.05 


1.75 


to 3.63 


0.8281 


-0.04264 


1.071 


1.027 


0.983 


RMLCA 




> 


3.63 


0.8281 





1.014 


1.014 


1.014 


R2LUA 







to 1.75 


0.8281 





1.005 


1.005 


1.005 


RMLUA 


0.10 


1.75 


to 3.75 


0.8281 


-0.04264 


1.118 


1.031 


0.944 


RMLCA 




> 


3.75 


0.8281 





1.005 


1.005 


1.005 


R2LUA 







to 1.75 


0.8281 





0.988 


0.988 


0.988 


RMLUA 


0.20 


1.75 


to 4.00 


0.8281 


-0.04264 


1.215 


1.040 


0.866 


RMLCA 




> 


4.00 


0.8281 





0.988 


0.988 


0.988 


R2LUA 







to 1.75 


0.8281 





0.970 


0.970 


0.970 


RMLUA 


0.30 


1.75 


to 4.25 


0.8281 


-0.04264 


1.310 


1.049 


0.787 


RMLCA 




> 


4.25 


0.8281 





0.970 


0.970 


0.970 


U2LUA 







to 1.75 


0.8281 





1.014 


1.014 


1.014 


U2LUA 


0.05 


1.75 


to 3.63 


0.8281 


-0.04264 


1.057 


1.013 


0.970 


U2LUA 




> 


3.63 


0.8281 





1.014 


1.014 


1.014 


U2LUA 







to 1.75 


0.8281 





1.005 


1.005 


1.005 


U2LUA 


0.10 


1.75 


to 3.75 


0.8281 


-0.04264 


1.091 


1.004 


0.916 


U2LUA 




> 


3.75 


0.8281 





1.005 


1.005 


1.005 


U2LUA 







to 1.75 


0.8281 





0.988 


0.988 


0.988 


U2LUA 


0,20 


1.75 


to 4.00 


0.8281 


-0.04264 


1.160 


0.985 


0.811 


U2LUA 




> 


4.00 


0.8281 





0.988 


0.988 


0.988 


U2LUA 







to 1.75 


0.8281 





0.970 


0.970 


0.970 


U2LUA 


0.30 


1.75 


to 4.25 


0.8281 


-0.04264 


1.228 


0.966 


0.704 


U2LUA 




> 


4.25 


0.8281 





0.970 


0.970 


0.970 


UMLUA 







to 2.0 


1.4873 





0.963 


0.963 


0.963 


UMLCA 


0.05 


2.0 


to 3.75 


1.4873 


-0.04264 


1.002 


0.962 


0.922 






> 


3.75 


1.4873 





0.963 


0.963 


0.963 


UMLUA 







to 2.0 


1.4873 





0.986 


0.986 


0.986 


UMLCA 


0.10 


2.0 


to 4.0 


1.4873 


-0.04264 


1.065 


0.985 


0.905 






> 


4.0 


1.4873 





0.986 


0.986 


0.986 



56 



TABLE 7 (Concluded) 



Area Type 
and 


£w 


Overall 
Accident Rate Range 
(accidents/MVM) 


h. 


tl 


Correction Factor, G 
for SN40 o 


Highway Type 


20 


40 


60 


UMLUA 
UMLCA 


0.20 


to 2.0 
2.0 to 4.5 
> 4.5 


1.4873 
1.4873 
1.4873 



-0.04264 



1.032 
1.190 
1.032 


1.032 
1.030 
1.032 


1.032 
0.869 
1.032 


UMLUA 
UMLCA 


0.30 


to 2.0 
2.0 to 5.0 

> 5.0 


1.4873 
1.4873 
1.4873 



-0.04264 



1.078 
1.315 
1.078 


1.078 
1.074 
1.078 


1.078 
0.834 
1.078 



ALT 0T = (AALL)(100-PRALL(KM)) 

100 

where ALTOT = Expected number of accidents afcer implementation 

of countermeasure KM 

AALL = Expected number of accidents if no countermeasure 
is implemented 

PRALL(KM) = Percent accident reduction for all accidents for 
countermeasure KM 

ALTOT is then separated into two components: ALFI and ALPD0 , where ALFI 
is the number of fatal and injury accidents remaining after implementation 
of the countermeasure and ALPD0 is the number of property-damage-only acci- 
dents remaining after the countermeasure is implemented. 

If for any countermeasure, Table 5 contains percent accident reduc- 
tion by one of the four accident breakdowns, these values will be used rather 
than the percent reduction for all accidents. The accident totals to which 
these percent reductions are applied for each category of the accident break- 
down used are obtained by the model in one of two ways; either (1) the total 
number of accidents, AALL , is separated into components by use of typical 
accident distributions available in the model, or (2) the user supplies the 
actual number of accidents in each category. The first course is followed 
if no accident data other than the total number of accidents are available. 
If the user does have detailed accident data for the site under analysis, 
he can supply the actual number of accidents in each category of the acci- 
dent breakdown being used; e.g., if the percent reduction by accident sever- 
ity is available in Table 5, the user can override the typical distribution 
of accident severities contained in the model and supply the actual number 
of fatal, injury, and property-damage-only accidents. This option gives 
the model great flexibility, since the user can perform a benefit-cost 
analysis using estimates when very little accident data are available or 
he can use detailed accident data for the site. 

Table 8 presents the distribution of accident severities used by 
the model for different area and highway types. The model assumes this 
same distribution of accident severities for all site types. These values 
were obtained from accident statistics for the entire state highway systems 
in the States of California, Michigan and Washington. The percentages in 
Table 8 are used by the model (if the user does not supply accident data 
by severity) to separate the total number of accidents, AALL , into two 
components — fatal plus injury, and property-damage-only. 



58 



TABLE 8 

DISTRIBUTION OF ACCIDENT SEVERITIES BY 
HIGHWAY TYPE AND AREA TYPE 

SOURCE : Compiled from accident statistics for the entire state highway 

systems of California, Michigan and Washington. The California 
and Washington data are for the period 1972-5 and the Michigan 
data are for 1971-4. 

Percent of All Accidents 



Fata 1-and- Injury Property-Damage -Only 

Highway Type Rural Urban Rural Urban 

Two-Lane, Uncontrolled Access 36.91 31.54 63.09 68.46 

Multilane, Uncontrolled Access 35.54 32.17 64.46 67.83 

Multilane, Controlled Access 35.49 31.41 64.51 68.60 



Table 9 presents the distribution of accident types used by the 
model for different site and area types. The model assumes this same dis- 
tribution of accident types for all highway types. This distribution is 
used to separate AALL into nine components, representing nine different 
accident types used in the model. 

The model assumes that 29.7% of all accidents occur at night and 
that the remaining 70.3% occur during daylight. These values were adapted 
from an hourly distribution of accidents in the 1975 edition of Accident 
Facts ,i/ assuming night to be represented by the hours of 7 p.m. to 6 a.m. 
Similarly, the model assumes that 16.26% of all accidents occur under wet- 
pavement conditions and the remaining 83.74% of accidents occur under dry- 
pavement conditions. The values were obtained from data obtained from manv 
states and presented in NCHRP Report 37.—' 

The final step performed by the model in determining the effective- 
ness of geometric and traffic control countermeasures is to determine the 
number of accidents remaining in each category of the accident breakdown 
used as: 

AL = (A) (100 - PR(KM)) 
100 

where AL = Expected number of accidents in a given category 

after implementation of countermeasure KM 

59 



A = Expected number of accidents in the category 
if no countermeasure is implemented 

PR(KM) = Percent accident reduction for accidents in a 
given category for countermeasure KM 

The accidents remaining after countermeasure implementation, AL , are 
totaled for all categories to obtain the total number of remaining accidents. 
Finally, if an accident breakdown from Table 5 other than by severity was 
used, the remaining accidents are separated into fatal-plus-injury and 
property-damage-only components, designated ALFI and ALPD0 , respectively. 
If an accident breakdown by severity from Table 5 was used, this final step 
is unnecessary because ALFI and ALPD0 are available directly. 



TABLE 9 



DISTRIBUTION OF ACCIDENT TYPES BY AREA TYPE AND SITE TYPE 



SOURCE : Adapted from References 1 and 10a, 



Percent of Accidents 







Rural 






Urban 








Non- 






Non- 






Highway 


Intersection 


Intersection 


Highway 


Intersection 


Intersection 


Accident Type 


Section 
3.43 


Site 


Site 


Section 
5.28 


Site 


Site 


Head-on 


4.40 


0.67 


6.11 


4.09 


Rear-end 


18.43 


19.07 


16.62 


30.39 


36.41 


21.94 


Sideswipe 


13.48 


13.89 


12.23 


6.34 


7.32 


4.99 


Rignt-angle 


11.86 


0.76 


43.46 


18.67 


0.64 


43.99 


Left-turn 


4.42 


3.13 


8.07 


6.64 


2.63 


12.26 


Parking- related 


4.50 


6.08 





15.20 


26.03 





Fixed-object 


21.10 


25.54 


8.46 


8.30 


11.60 


3.61 


Pedestrian 


1.10 


1.21 


0.77 


2.30 


2.40 


2.16 


Other 


21.68 


25.92 


0.72 


6.88 


6.86 


6.96 



60 



G. Influence of APT on Accident Rate 

The analyses of Phase I found that ADT had an influence on acci- 
dent rates for some area type-highway type combinations. However, the 
information obtained was not sufficient to quantify the effects of the 
moderate changes in ADT likely to occur from year to year on an analyzed 
facility. Consequently, the model employs the regression results developed 
by Fee.***/ 

Within the model, an adjustment factor for ADT is evaluated for 
each year and is applied to adjust the accident rate from the previous 
year to the year being calculated. The adjustment factor is calculated 
in subroutine DTADJ. It has the symbol name DTJST and is calculated as 
the ratio: 

DTJST = AJDT/AJTLD 
where AJTLD = accident rate based on ADT in previous year, 

AJDT = accident rate in current year, 
calculated from the referenced regression results as a cubic in ADT: 

AJDT = AT3*ADT**3 + AT2*ADT**2 + ATl*ADT + ATO . 

The coefficients depend on area type and highway type and are 
double subscripted for those designations. The ADT employed is restricted 
in range so that if the site value falls outside that range it is replaced 
in the equation with the appropriate limit value. The coefficients and 
the limit ADT are shown in Table 10. 

H. Sequence of Processing Accidents and Accident Costs 

The model requires that the analyses at any site begin with the 
average number of accidents at the site for the year prior to installation 
of a count ermeasure (the "zeroth" year) . The zeroth year estimate can be 
based on historical data or on the program user's professional judgement. 
The estimate can consist of total accidents or, separately, the property- 
damage-only accidents and the injury-plus- fatal accidents. 

The subsequent processing dealing with accident numbers or rates 
always employs fractional or incremental changes. This logic preserves the 
influence of rates or proportions at the analyzed site that may be markedly 
different from the average for sites with similar area and highway types. 



61 



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The first step in accident cost calculations is taken in sub- 
routine ACC0ST where two average costs are calculated. One is for property- 
damage-only accidents; the other is for combined injury-plus-fatal accidents, 
The calculations employ the costs of a fatality, an injury, and the per 
vehicle property damage. The calculations also employ the average numbers 
of fatalities, injuries and vehicles involved per accident type, which are 
a function of area type and highway type. The proportions of fatal and of 
injury accidents also depends on area type and highway type. All these 
factors are obtained from system files. The cost calculations also employ 
the separate cost weight factors for fatalities, injuries and property 
damage supplied by the user. The above calculations and results are in- 
dependent of countermeasures and the subsequent course of events at the 
site. All calculations that follow depend on individual countermeasures 
or on the future of the base condition. 

The following sequence of calculations deals with the accident 
consequences and costs associated with a count ermeasure or with the base 
conditions at the site analyzed. All computer program logic is contained 
in the large subroutine C0STS, which deals with one countermeasure (or the 
base condition) at a time. The following description deals with the 
accident-related logic. 

The first major step in C0STS is to calculate the zeroth year 
accidents with the countermeasure incorporated. (If the base case includes 
a prior decision to modify the surface and consequently skid number, this 
change will be included.) The revision of zeroth year accidents due to 
geometric and traffic control countermeasures is calculated in subroutine 
GREDU. (Preparation for this calculation is made in preceding subroutines.) 
After leaving GREDU, where the distribution of severities may change, a cost 
per accident averaged over all accident severities is calculated for subse- 
quent use. Also, the remaining accident number is converted to a rate. 

At this point, a calculation is made for additional zeroth year 
accidents associated with countermeasure construction, if any. If the 
countermeasure construction requires lane closure the costs of accidents 
due to that construction are entered as part of accident costs associated 
with the countermeasure, even though they occur in the zeroth year. 

The next major step, still for the zeroth year, is to adjust the 
accident rate for the change in skid number. Skid number will change in 
the zeroth year for countermeasures that change the surface, or, for the 
base case if there has been a prior decision to modify the surface. After 
adjustment for skid number the accident rate is the rate that would have 
occurred in the zeroth year if the countermeasure being processed had been 
installed and operating for the entire year. Also available is the average 
cost per accident with the countermeasure installed. 



63 



Subsequent processing of accidents and accident costs deals with 
1 year at a time for future years 1, 2, etc., through the final year of the 
period of analyses. For each year the accident rate in the preceding year 
is the starting point. The rate is adjusted for the effects of change in ADT. 
Then it is incremented for the change in skid number. Finally, the accident 
rate, the ADT, the site length, accident increases due to countermeasure 
construction during the year, and the average cost per accident are combined 
to obtain the accident costs for the year. These costs are subsequently 
discounted using economic equations and assembled to provide the equivalent 
uniform annual accident costs with the countermeasure analyzed. 



64 



VII. SUBSCRIPT RANGES FOR COUNTERMEASURES 



Subscripts are used to identify countermeasures in the data files 
and within the computer program. These subscripts are used in the input 
data to specify the particular countermeasures to be included in the analysis. 
Certain subscript ranges are reserved in the model for specific types of 
countermeasures. The boundaries of the reserved subscript ranges are de- 
fined by the variables KSM, KM2, KM3, K2 and KMAX in the following manner: 

The subscript 1 is reserved for the initial, base condition, 
i.e., the "as is" or "as planned" condition. 

Subscripts 2 through KSM are reserved for the countermeasures 
that involve modification of the pavement surface, such as surface courses, 
surface treatments and chip and seal coats. 

Subscripts (KSM + 1) through (KM2 - 1) are reserved for the 
geometric and traffic control countermeasures incorporated in the model 
(see Section VI. B) that do not require additional right-of-way. 

Subscripts KM 2 through (KM3 - 1) are reserved for counter- 
measures that may require additional right-of-way, including both those in- 
corporated in the model and those supplied by the user. 

Subscripts KM3 through (KM2 + K2 - 1) are reserved for geometric 
and traffic control countermeasures, supplied by the user, that do not 
require additional right-of-way. 

. Subscripts (KM2 + K2) through (KM3 + K2 - 1) are reserved for 
right-of-way costs, lives, etc. 

Subscripts (KM3 + K2) through (KMAX - 1) are reserved for addi- 
tional geometric and traffic control countermeasures, supplied by the user, 
that do not require additional right-of-way. 

Subscript KMAX is the largest subscript and is reserved for 
use with Subroutine SIG0, which is intended to calculate whether significant 
accident reduction savings are possible at the analysis site. This sub- 
routine is not included in the current version of the model, but could be 
added. Therefore, Subscript KMAX is not currently used by the program logic. 

The specific values presently incorporated in the model for the 
variables that define the boundaries of the subscript ranges are: 



65 



KSM = 21 
KM2 = 95 
KM3 = 127 
K2 = 42 
KMAX = 180 

These values result in the following boundaries for the subscript 
ranges: 

Subscript Range Type of Countermeasure 

1 Initial, baseline condition. 

2-21 Countermeasures involving pavement surface modification. 

22 - 94 Geometric and traffic control countermeasures incorporated 

in the model that do not require additional right-of-way, 

95 - 126 Geometric and traffic control countermeasures that may 

require additional right-of-way (Subscripts 95 through 
120 are reserved for countermeasures incorporated in 
the model and Subscripts 121 through 126 are reserved 
for countermeasures supplied by the user) . 

127 - 136 Geometric and traffic control countermeasures supplied 

by the user that do not require additional right-of-way. 

137 - 168 Right-of-way costs, lives, etc. 

169 - 179 Additional geometric and traffic control countermeasures, 

supplied by the user, that do not require additional 
right-of-way. 

180 Maximum subscript. 

If more countermeasures are incorporated in the model in a future revision, 
the values of KSM, KM2, KM3, K2 and KMAX must be adjusted accordingly. 



66 



VIII. INPUT REQUIREMENTS 



This section presents the input requirements for the benef it- 
cost model. The input data items are presented and discussed to the ex- 
ter.t necessary for a user to determine their values. For a complete dis- 
cussion of the manner in which each variable is used in the model, the 
reader is referred to other sections of this report. 

Table 11 identifies the input data that are to be supplied by 
the user each time the benefit-cost program is run. Additional input to 
the program is obtained from the cost files that are maintained by the 
user. The table indicates whether each of the input data items are manda- 
tory or optional. Many of the optional items are included to give the 
user an opportunity to change the value of a variable from the files for 
a specific analysis without disturbing the long-term system value. The 
comment column of the table provides detailed information needed by the 
user to select values for the input variables. 

Table 11 is divided into three sections which deal with gen- 
eral input data, site characteristics, and countermeasures. The follow- 
ing discussion of input requirements is organized in the same manner. 



A, General Input Data 

The general input data items perform two functions: (1) provide 
information to be printed in output headings and (2) control the type of 
analysis performed. 

The sequence number, date of analysis and end date of the zeroth 
year are included because they appear in output headings. The decimal 
interest rate appears in the output heading, and is also used in the 
analysis to determine discount factors. 

Variables FPD( ), FIA( ), FFA( ), and FUTC( ) are weight factors 
that can be used to modify the costs of accidents and user time delays in- 
corporated in the model. JPER( ) is used to select the longer or shorter 
applied life for use as the analysis period, when countermeasures with dif- 
ferent applied lives are compared. MXYR sets a limit on the length of the 
analysis period for all countermeasures considered. Finally, CFAS and 
CCAS are variables that are not presently used, but could be incorporated 
in a future version of the model. 



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74 



B. Site Characteristics 

This portion of the input data contains several basic site param- 
eters such as the site description, state and region, area type, highway 
type, site type, site length, fraction of time with wet pavement and average 
annual precipitation. 

The user must specify whether or not a prior decision to resurface 
the facility has been made and must estimate the remaining life of the facil- 
ity and the remaining time period before the facility will be resurfaced and/ 
or rebuilt. 

The user has the option of specifying the current skid number of 
the facility. However, default values of skid number are available from the 
files in the event that the user does not have this information available. 

The ADT of the facility in both the zeroth year and each subsequent 
year must be specified using one of the three options described in the table. 

The user must also specify the expected total number of accidents 
per year for the facility in its present condition. The user may supply a 
more detailed description of the accident experience, but if additional acci- 
dent data are not available, the required accident frequencies can be esti- 
mated using default accident distributions contained in the program. 



C. Count ermeasures 

The user must specify one or more countermeasures for analysis by 
the program. Usually, the user will desire to compare several options for 
reduction of accidents at a given site. The only information that the user 
must supply concerning each countermeasure are the countermeasure number, 
countermeasure name, number of units of the countermeasure to be installed 
and a code representing the vulnerability of the countermeasure to resurfac- 
ing and rebuilding. However, the user also has the option of replacing the 
values of applied life, salvage value, capital costs and maintenance and 
operating costs available from the files. 

The model has the capability of including, in the economic anal- 
ysis, the user costs for delay time and excess fuel consumption due to 
reduced traffic service during construction of the countermeasure. Four 
variables must be identified by the user to exercise this option: (1) the 
number of days when traffic service is reduced due to construction, (2) the 
type of construction zone configuration, (3) the length of the construction 
zone and (4) the hours of the day during which traffic service is reduced. 
This option can be bypassed by setting the number of days with reduced traf- 
fic service equal to zero. 

75 



Finally, the user can replace the percent accident reductions in- 
corporated in the model (see Section VI. E), by specifying the percent acci- 
dent reductions for one of five accident breakdowns: all accidents, 
accidents by severity, accidents by accident type, accidents by pavement 
conditions or accidents by light condition. 






76 



IX. SUMMARY OF OUTPUT 



The computer program provides a printed output for each case that 
is analyzed. This output presents all of the economic data required by a 
highway engineer or administrator to make planning and budgeting decisions, 
and the output will serve as a permanent record of the analysis results. 
This section of the report presents the output formats used by the model 
and explains all of the output data. 

The input data supplied by the user is printed in an expanded 
card format. This output is very important since it will contain the 
numerical information where the user has overridden standard file values. 

The benefit-cost model produces output in two forms corresponding 
to the two stages of the benefit-cost analysis: countermeasure economic 
feasibility analysis and project formulation. The difference between these 
stages, as explained in Section IV. B, is that in the economic feasibility 
analysis each alternate countermeasure is compared with the initial base 
condition, while in the project formulation stage the countermeasures are 
compared incrementally, in order of increasing capital costs. When a counter- 
measure is accepted in project formulation (incremental benefit/cost ratio 
greater than one), it becomes the base for subsequent calculations. Since 
the economic data that must be presented are similar, the headings and print- 
out formats used for each stage of the analysis are identical, except for 
the main heading at the top of each page. The output from the economic 
feasibility and project formulation analyses are presented on consecutive 
printout pages. 

Figure 8 illustrates the output format that is used for both 
economic feasibility and project formulation. Lines 1 through 12 of the 
printout are a heading block containing general information identifying 
the analysis site and the type of analysis. Beginning with line 18, the 
printout is organized into groups of three lines labeled BASE, ALTERNATE 
and ALT-BASE, Each group of lines represents a comparison between one 
alternate coutermeasure and the appropriate base condition. In each stage 
of the analysis, these groups of three lines are repeated as many times as 
necessary to compare each alternative with the appropriate base condition. 
As an example, consider lines 18 to 20, the first group shown in Figure 8. 
All cash flows for the base and alternate condition are listed on lines 18 
and 19, respectively. Line 20 contains the differences between these cash 
flows, expressed as the cash flow for the alternate minus the cash flow for 
the base. 

The data items presented on the output are numbered 1 through 46 
in Figure 8, Each of these items is discussed below in detail. 



77 






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78 



A. Heading Block 

The following information is presented in the heading at the be- 
ginning of each stage of the analysis. 

Item 1 - Main Heading . The heading COUNTERMEASURE ECONOMIC 
FEASIBILITY or PROJECT FORMULATION appears at the top of the page to identify 
the stage of the analysis for which results are presented. 

Item 2 - State . This item is a two-character code identifying 
the state in which analysis site is located. This code, whose computer 
symbol is KSTAT, is assigned by the user as input data. 

Item 3 - Intrastate Region . This item is a two-character code 
identifying a region within the state in which the analysis site is located. 
This code, whose computer symbol is KSTAR, is assigned by the user as input 
data. 

Item 4 - Analysis Site . This space on the printout is reserved 
for the name or description of the analysis site, as specified by the user. 
It appears on the printout on two lines, with a maximum of 40 characters 
on each line. 

Item 5 - Fraction of Wet— Pavement Time . This item is the fraction 
of time with wet pavement at the analysis site and is specified by the user 
as input. The computer symbol for this fraction is FWET. 

Item 6 - Average Annual Precipitation . The average annual pre- 
cipitation for the region in which the analysis site is located is printed 
in space 6. This quantity is specified by the user as input and is repre- 
sented in the computer by the symbol APREC. 

Item 7 - Prior-Decision Job Number . If a prior decision has been 
made to resurface or rebuild the facility, the job number assigned by the 
user for that decision will appear in space 7. Thus, if a job number appears 
here, it indicates that the benefit-cost analysis has included the impact 
of the prior decision. If no prior-decision job number appears, then the 
facility has been analyzed in its present condition. A complete discussion 
of the treatment of prior decisions in the model is found in Section V.H 
of this report. 

Item 8 - Decimal Interest Rate . The interest or vestcharge rate 
used in the analysis is presented here in decimal form. This quantity, 
represented in the computer by the symbol V, is the minimum rate of return 
that is acceptable to the user. 



79 



Items 10, 11, 12 and 13 - Cost Weight Factors . The items pre- 
sented here are the weight factors for costs of property damage only acci- 
dents, injury accidents, fatal accidents and user time delay, respectively. 
These variables have a default value of 1.0, which is used unless the user 
specifies some other value. The cost weight factors are displayed on the 
output to provide a permanent record of any adjustments made during the 
analysis to the costs obtained from the cost files. See Section V.J for 
a description of these factors. 

Item 14 - Length of Analysis Period . This space contains the 
label LONG or SHORT to identify whether the longer or shorter analysis per- 
iod has been used when countermeasures with unequal service lives are com- 
pared. As stated in Section V.D, the choice of analysis periods is deter- 
mined by the value of the variable JPER( ). In the default case, the pro- 
gram sets JPER( ) = 2 and uses the longer of the two analysis periods. 
The user has the option of setting JPER( ) = 1 and using the shorter analy- 
sis period, or of performing the analysis twice, using each of the two 
periods. 

Item 15 - Analysis Number . The analysis number is a 14-digit 
number of the form: XX XX XXXX XXXXXX. The first two digits of the 
analysis number identify the state in which the analysis site is located. 
The next two digits identify the appropriate region within that state. The 
next four digits identify the year in which the analysis was conducted, and 
the final six digits are a sequence number assigned to the analysis. The 
analysis number is intended as a unique designation that can be used to 
identify the particular analysis in a state's file. 

Item 16 - Analysis Date . This item is the month, day and year 
on which the analysis was conducted. It is the form: XX XX XXXX where 
the first two digits represent the month (01 = January,..., 12 = December), 
the next two digits represent the day (01,..., 31), and the final four 
digits represent the year (1977, 1978, 1979, etc.). 

Item 17 - Date Zeroth Year Ends . This item is the final date of 
the zeroth year of the analysis. The zeroth year is the year during which 
the countermeasure is implemented. This date is specified by the user as 
input and is presented in the same format as Item 16. 

Item 18 - Minimum Equivalent Uniform Annual Accident Cost . The 
minimum equivalent uniform annual accident cost is not incorporated in the 
current version of the model, but a space is reserved for it on the output 
should it be added in a subsequent revision. This quantity represents the 
lowest total accident cost that would be possible if the most effective 
available countermeasure were implemented. This quantity will be used in 
Subroutine SIG to determine whether any significant accident savings are 
possible at the analysis site. 

30 



B. Comparisons of Base and Alternate Conditions 

Cash flows and other relevant data for the each pair of base and 
alternate conditions analyzed are presented on the printout lines labeled 
BASE and ALTERNATE. The differences between these cash flows are used in 
the calculation of benefit/cost ratio and are presented on the line, ALT- 
BASE. The following discussion describes each item found on these three 
lines . 

Items 19 and 20 - Countermeasure Description . These spaces contain 
20 character titles identifying the countermeasures compared on the lines. 
The user specifies a name for each countermeasure selected as input to the 
model. In the economic feasibility stage, the base case will always be 
the present condition of the facility (or its projected condition based on 
prior decisions), and will be identified in item 19 by the designation 
EXISTING. The alternate will be a user-selected countermeasure with a user- 
selected name. In the project formulation stage, the base will be the 
least expensive countermeasure, but the initial base may be replaced by a 
more cost-beneficial countermeasure as the incremental analysis proceeds. 

Items 21 and 22 - Number of Countermeasure Units . Items 21 and 
22 identify the number of units of each countermeasure required for the 
base and alternate cases. These values are specified by the user and their 
units must be compatible with the unit costs available in the cost files. 
The numbers of units are used to determine the capital cost of each counter- 
measure from the cost files. When the existing condition is used as the 
base, item 21 will be zero, but in all other situations items 21 and 22 are 
non-zero. The computer symbols for items 21 and 22 are UN(KB) and UN(KC), 
respectively. 

Item 23 - Period of Analysis . This data item is the period of 
analysis (in years) that is used to compare the base and alternate conditions. 
It is printed on the third (ALT-BASE) line and its computer symbol is IA. 
The period of analysis is determined by the program for each base and alter- 
nate countermeasure, and depends on their normal service lives and on the 
user's selection of the long or short option for length of analysis period. 

Items 24, 25 and 26 - Equivalent Uniform Annual Capital Costs . 
Items 24 and 25 are the equivalent uniform annual capital costs for the 
base and alternate conditions, respectively. These are determined by an- 
nualizing all capital expenditures for each countermeasure. The equivalent 
uniform annual capital cost for the existing condition is zero except in 
two cases. First, if a prior decision has been made to resurface (or to 
resurface as part of rebuilding), the capital cost for the resurfacing ap- 
pears in the base case when an alternative resurfacing countermeasure is 
evaluated in economic feasibility. If the alternative surface is accepted, 
its capital costs in subsequent calculations for project formulation are 
reduced in accord with the capital commitment from the prior decision. 

81 



In the second situation, base case capital costs will appear in 
economic feasibility calculations when a resurfacing countermeasure would 
last longer than the existing surface course. In this situation, the future 
capital cost of the base case resurfacing is discounted and distributed 
over the entire period until its end of life. There is no influence in 
project formulation calculations. 

Item 26 is the difference between the equivalent uniform annual 
capital costs for the alternate and base conditions and is used as the de- 
nominator of the benefit/cost ratio. The computer symbols for these three 
capital costs are UCC(l), UCG(2), and UCC(3), respectively. 

Items 27, 28 and 29 - Equivalent Uniform Annual Maintenance and 
Operating Costs . The meanings of these costs are directly analogous to 
the capital costs discussed above, except that they represent the main- 
tenance and operating costs. The maintenance and operating costs are 
always non-zero, even for the existing condition. The computer symbols 
for items 27, 28 and 29 are EUAM0(1), EUAM0(2), and EUAMI&(3), respectively. 

Items 30, 31 and 32 - Equivalent Uniform Annual User Costs . The 
meanings of these costs are directly analogous to the maintenance and operat- 
ing costs discussed above, except that they represent user costs associated 
with construction or other implementation. The computer symbols for items 
30, 31 and 32 are EUAUC(l), EUAUC(4) and EUAUC(3), respectively. 

Items 33, 34 and 35 - Equivalent Uniform Annual Accident Costs . 
The meanings of these costs are directly analogous to the maintenance and 
operating costs discussed above except that they represent the cost of 
traffic accidents at the analysis site. The computer symbols for items 
33, 34 and 35 are EUAAC(l), EUAAC(2) and EUAAC(3), respectively. 

Item 36 - Net Return . This quantity is the sum of the equivalent 
uniform annual costs shown on the ALT-BASE line for capital outlays, main- 
tenance and operating costs, user costs and accident costs. The net return 
is represented in the computer program by the symbol RN. 

Items 37, 38 and 39 - Undiscounted Capital Outlays . Items 37 
and 38 are the undiscounted capital costs for the base and alternate con- 
ditions. Each of these quantities is the sum of the values of all capital 
outlays at the time they occur. When the only capital outlay occurs during 
the zeroth year, these quantities are simply the present value of the equiv- 
alent uniform annual capital costs given in items 24 and 25. Item 39 is 
the difference between the undiscounted capital outlays for the alternate 
and base conditions. The computer symbols for items 37, 38 and 39 are 
C0LD(1), C0LD(2), andC0LD(3), respectively. 



82 



Items 40) 41 and 42 - Undiscounted Average Maintenance and Operat - 
ing Expenses . Items 40 and 41 are the average undiscounted maintenance and 
operating expenses per year for the entire analysis period for the base and 
alternate conditions. These items are the sums of all maintenance and operat- 
ing expenditures during the analysis period divided by the number of years 
in the analysis period. Item 42 is the difference between items 41 and 40. 
The computer symbols for items 40, 41 and 42 are AM0(1), AM0(2) and AM0(3), 
respectively. 

Items 43 and 44 - Applied Lives of Countermeasures * These spaces 
contain the applied lives for the base and alternate conditions. The applied 
life of a countermeasure can differ from the normal service life, as ex- 
plained in Section V # D, The computer symbols for Items 43 and 44 are LAF(KB) 
and LAF(KC), respectively. 

Item 45 - Benefit/Cost Ratio . The benefit/cost- ratio, represented 
by the computer symbol BCR(KC), is formed from the equivalent uniform annual 
cash flows shown on the printout, using the definition presented in Section 
V.B. 

Item 46 - Acceptance of Alternatives . If the benefit/cost ratio 
is larger than 1.0, the alternate is accepted and YES is printed on the 
output. If the benefit/cost ratio is smaller than 1.0, the alternate is 
rejected and NO is printed. In the economic feasibility stage, acceptance 
of an alternate countermeasure means that the alternate is preferable to 
the existing condition and should be included in the project formulation 
state. If a countermeasure is rejected in the economic feasibility stage, 
it is not considered further. If an alternate is accepted in the project 
formulation stage, it becomes the new base to which subsequent alternates 
are compared. The last alternate for which a YES is found in the acceptance 
of alternatives column on the project formulation printout is the best in- 
vestment of capital. 



83 



X. EXAMPLE OF BENEFIT-COST ANALYSIS 



This section of the report presents the solution of an example 
problem using the benefit-cost model. Section A explains the example 
problem to be solved. The problem presented is completely hypothetical, 
but is typical of the kinds of problems that can be solved using the model. 
Section B presents the values of all input variables to the model including 
both the data supplied by the user and data obtained from the files. The 
outputs from the economic feasibility and project formulation stages of the 
analysis are presented in Section C. 



A. Example Problem 

A state highway department has identified the 2-mile portion of 
State Route 55 between Mileposts 15.0 and 17.0 as one of several highway 
sections in the state with adverse accident experience resulting from low 
skid resistance, among other causes. Route 55 is a two-lane rural highway 
whose current ADT of 5,000 is expected to increase at a linear rate of 3% 
per year. The pavement currently has a skid number at 40 mph of 32.0. The 
section is exposed to wet-pavement conditions 257» of the time, on the aver- 
age. The section currently experiences 19 accidents per year, correspond- 
ing to an accident rate of 5.21 accidents per million vehicle-miles. 

The state is considering three alternate counter-measures to reduce 
the accident experience for this highway. The first countermeasure, desig- 
nated as countermeasure number 2, is to resurface the section^with a normal 
asphalt concrete surface course. Normal resurfacing is assumed to cost 
$12,500 per mile and will initially increase the skid number at 40 mph to 
66.0. The skid number will decrease with traffic wear after installation 
according to the following relationship:^' 

SN = 66.0 - 8.3 in (CT/10 5 ) 

where SN = Skid number at 40 mph, and 

CT = Cumulative number of vehicle passes, 

until reaching a constant final value of 25.0. 

The second countermeasure, designated countermeasure Number 3, con- 
sists of resurfacing with a special asphalt concrete surface course using 50% 
lightweight aggregate. The advantage of the special surface course is its 
superior skid resistance qualities. Special resurfacing is assumed to cost 
$20,000 per mile and will initially increase the skid number at 40 mph to 43.0. 
However, the skid number will increase from its initial value, rather than de- 
crease, with traffic exposure. The relationship for the increase of skid 
number at 40 mph for the special surface course is:— 

84 



SN = 43.0 + 2.428 jtn (CT/10 5 ) 

with a maximum SN of 70.0 

The final countermeasure is the improvement of warning signs on 
the section, designated as countermeasure number 28 in Table 5. State high- 
way engineers have determined that this countermeasure would require improve- 
ment of 16 signs at $200 per sign. 

It is assumed that both of the resurfacing counter-measures can be 
constructed in 4 working days. The lanes in each direction at a time will be 
closed for 1/2 day at each of four 0.5 mile work sites with traffic operating 
in alternating directions in the other lane. The reduction in traffic service 
will begin each day at 8 AM and cease at 4 FM. User delay time is estimated 
at $3.00 per hour and gasoline costs at $0.60 per gal. Installation of warn- 
ing signs will not involve any reduction in traffic service. 

The resurfacing countermeasures have normal service lives of 15 
years, while the warning signs have service lives of 5 years. It is assumed 
that no resurfacing or rebuilding will interrupt these service lives and that 
norfi of the countermeasures has any salvage value at the end of its useful 
life. It is also assumed that the user elects the longer period of analysis 
when countermeasures with different service lives are compared. Finally, it 
is assumed that this highway section costs $500 per mile per year to maintain 
and that none of the countermeasures influence this maintenance cost. 



B. Input Data for Example Problem 

The user should begin the solution of a problem by specifying the 
values for the input variables. Table 12 presents the values of the input 
variables for the example problem presented above. Definitions of these 
variables are presented in Sextion VIII of this report. Table 12 includes 
all variables that can be used as input to the program. The reader will note 
that many of the input variables have a value of zero. These variables can 
be used to supercede default variables contained in the system files* In 
this example, we have elected to use the default values in the system files. 
Therefore, zero values have been indicated at appropriate places in Table 12. 
In actual practice a zero or a blank could be input for these variables. In 
this example, we have elected to use the default values in the system files. 
In addition, most of these variables are contained on optional input cards 
that do not need to be used each time the program is run if all input var- 
iables on the card are zero or blank. 

Table 13 presents a partial list of the values of input variables 
obtained by the program from the system files in solving the example problem. 
Definitions of each of these variables are contained in Appendix G. 



85 



TABLE 12 



INPUT DATA SUPPLIED BY USER FOR EXAMPLE PROBLEM 



Data Item 



Symbol 



Value 



Sequence Number 

Analysis Date 

End Date of Zeroth Year 

Decimal Interest Rate 

Subscript for Following Five Codes 

Weight Factor for Property -Damage-Only Accident 

Costs 
Weight Factor for Injury Accident Costs 
Weight Factor for Fatal Accident Costs 
Weight Factor for User Delay Costs 
Code for Analysis Period 
Upper Limit on Period of Analysis (Years) 
Coefficient for Fraction of Accident Costs Saved 

in Test for Significant Savings 
Coefficient for Fraction of Accident Costs Saved 

in Test for Significant Savings 
Site Description 

Numerical Code for State 

Numerical Code for Region 

Area Type 

Highway Type 

Site Type 

Site Length (miles) 

Fraction of Time with Wet Pavement 

Average Annual Precipitation (in.) 

Code for Prior Decision to Resurface 

Prior Decision Job Number 

Number of Units of Surface Course Planned as a 

Result of Prior Decision 
Final Capital Worth per Unit of Surface Course 

Planned as a Result of Prior Decision 
Normal Remaining Life of Facility 
Number of Years Until Scheduled Rebuilding 
Number of Years Unit Scheduled Resurfacing 
Current Skid Number 
Current or Planned Surface Type 
ADT for Majority Facility in Zeroth Year 



V 
NVAR 
FPD(NVAR) 



028964 
01 31 1977 
12 31 1978 
0.06 
1 
Default Value 



= 1 



FIA(NVAR) Default Value 
FFA(NVAR) Default Value 
FUTC(NVAR) Default Value 
JPER(NVAR) Default Value 
MXYR Default Value 

CCAS 

CFAS 



1 
1 
1 
2 
20 





STATE ROUTE 55 




MP 


15.0-17.0 


KSTAT 




01 


KSTAR 




01 


IATYP 




1 


IHTYP 




1 


ISITE 




1 


TLGH 




2.00 


FWET 




0.25 


APREC 




52.0 


IRS 








UN(D 



FCW(l) 





LIFF 


25 


LIFRB 


15 


LIFRS 


15 


SNY0 


32.0 


KWS 


2 


TIM 


5000 



86 



TABLE 12 (continued) 



Data Item 



Symbol 



Value 



ADT for Secondary Facility in Zeroth Year TIS 

Percent Compounded Growth Rate of ADT for Major TMGC 

Facility 

Percent Linear Growth Rate of ADT for Major TMGL 3 

Facility 

Percent Compounded Growth Rate of ADT for Secon- TSGC 

dary Facility 

Percent Compounded Growth Rate of ADT for TSGL 

Secondary Facility 

ADT of Major Facility in Each Year ADTM( ) ALL = 

ADT of Secondary Facility in Each Year ADTS( ) ALL = 

Total Number of Accidents AALL 19 

Total Number of Fatal and Injury Accidents AFI 

Total Number of Property -Damage-Only Accidents APD0 

Total Number of Head-On Accidents AH0 

Total Number of Rear-End Accidents ARE 

Total Number of Side-Swipe Accidents ASS 

Total Number of Right-Angle Accidents ARA 

Total Number of Left-Turn Accidents ALT 

Total Number of Parking-Related Accidents APR 

Total Number of Fixed-Object Accidents AF0 

Total Number of Pedestrian Accidents APED 

Total Number of Other Accidents A0TH 

Total Number of Wet -Pavement Accidents AWET 

Total Number of Dry-Pavement Accidents ADRY 

Total Number of Nighttime Accidents ANIT 

Total Number of Daytime Accidents ADAY 



Data Item 



Symbol 



KM=2 



Value 



KM=3 



KM=28 



Count ermea sure Number 
Countermeasure Name 



KM 



Number of Units of Counter- 
measure UN (KM) 

User-Supplied Capital Outlay 

Per Unit of Countermeasure SCAPC(KM) 

Applied Life of Countermeasure LAF(KM) 

Final Capital Worth of 

Countermeasure After FCW(KM) 
1AF(KM) Years 



2 

NORMAL 

RESURFACING 

2.0 






SPECIAL 
RESURFACING 







28 

WARNING 
SIGNS 

16.0 






TABLE 12 (continued) 



Data Item 



Symbol 



KM=2 



Value 



KM=3 



KM=28 



User-Supplied Maintenance 
and Operating Expenses 
Due to Countermeasure 

User-Supplied Annual Rate of 
Change of Maintenance 
and Operating Expenses 

User-Supplied Upper Bound on 
Maintenance and Operating 
Expenses 

Time When Traffic Service is 
Reduced Due to Counter- 
measure Construction on 
Length ZLGH(KM) 

Type of Construction Zone 
Configuration 

Length of Construction Zone 

Code for Construction 
Schedule 

Percent Reduction for All 
Accidents 

Percent Reduction for Fatal 
and Injury Accidents 

Percent Reduction for Pro- 
perty-Damage-Only Accidents 

Percent Reduction for Head- 
On Accidents 

Percent Reduction for Rear- 
End Accidents 

Percent Reduction for Side- 
Swipe Accidents 

Percent Reduction for Right- 
Angle Accidents 

Percent Reduction for Left- 
Turn Accidents 

Percent Reduction for Park- 
ing Related Accidents 

Percent Reduction for Fixed- 
Object Accidents 

Percent Reduction for 
Pedestrian Accidents 

Percent Reduction for Other 
Accidents 



SCAM0(KM) 
SSMA0(KM) 
SMA0M(KM) 
TDUR(KM) 

KZOW(KM) 



ZLGH(KM) 
KCSCD(KM) 


0.5 
5 


0.5 
5 






PRALL(KM) 











PRFI(KM) 











PRPD0(KM) 











PRH0(KM) 











PRRE(KM) 











PRSS(KM) 











PRRA(KM) 











PRLT(KM) 











PRPR(KM) 











PRF0(KM) 











PRPED(KM) 











PR0TH(KM) 












88 



TABLE 12 (concluded) 



Va lue 



Data Item 

Percent Reduction for Wet- 
Pavement Accidents 

Percent Reduction for Dry- 
Pavement Accidents 

Percent Reduction for Night' 
time Accidents 

Percent Reduction for Day- 
time Accidents 



Symbo 1 


KM=2 


KM=3 


KM=28 


PRWET (KM) 











PRDRY (KM) 











PRNIT(KM) 











PRDAY (KM) 












S9 



TABLE 13 



PARTIAL LIST OF DATA FROM SYSTEM FILES FOR EXAMPLE PROBLEM 



Data Item 

Cost File Dates 

Average Number of Vehicles Per Property- 
Damage -Only Accident 

Average Number of Injuries Per Injury Accident 

Average Number of Fatalities Per Fatal Accidents 

Cost of Property-Damage-Only Accident Per 
Involved Vehicle 

Cost Per Injury 

Cost Per Fatality 

Cost Per Vehicle-Hour of Delay 

Cost Per Gallon of Fuel 

Average Fuel Consumption (gal/vehicle-hr) at Idle 

Average Annual Maintenance and Operating Cost Per 
Mile in Area Type IATYP and Highway Type IHTYP 

Percent of All Accidents Which are Fatal and 
Injury Accidents 

Percent of All Accidents Which are Property- 
Damage-Only Accidents 

Average Skid Number for Area Type IATYP 

Expected Increase in Accident Rate During 
Countermeasure Construction 



Symbol 



Value 







09 01 1976 


AP1(1) 




1.71 


AP2(1) 




1.66 


AP3(1) 




1.22 


CT1 




300 


CT2 




7300 


CT3 




200700 


CVHD 




3 


CFUEL 




0.60 


CIDLE 




0.0376 


ACMA0(1, 


,1) 


500 


PFI(1,1, 


,1) 


36.91 


PPD0(1,1,D 


63.09 


SBAR(l) 
ADR 




46.0 
1.068 



Value 



Data Item 

Site Type for Which Geometric or Traffic 
Control Countermeasure Was Evaluated 

Area Type for Which Geometric or Traffic 
Control Countermeasure Was Evaluated 

Highway Type for Which Geometric or Traffic 
Control Countermeasure Was Evaluated 

Fraction of Time Pavement Were Wet at Site 
Where Geometric or Traffic Control Counter- 
measures Were Evaluated 

Normal Life (years) of Countermeasure 

Code for Vulnerability to Resurfacing and 
Rebuilding 

Standard Capital Outlay Per Unit for 
Countermeasure 

Net Salvage Value Per Unit of Countermeasure 

Maintenance and Operating Expense Due to 
Countermeasure 



Symbol 


KM=2 


KM=3 


KM=28 


JSITE(KM) 








1 


JATYP (KM) 








1 


JHTY? (KM) 








1 


CAPFW(KM) 








0.13 


LIFC(KM) 
TRL (KM) 


15 
2.10 


15 
2.00 


5 
1.99 


CAPC(KM) 


12500 


20000 


200 


SALV(KM) 
CMA0(KM) 















90 



TABLE 13 (concluded) 



Value 



Data Item 

Rate of Change of Maintenance and Operating 

Expenses 
Upper Bound on Maintenance and Operating 

Expenses 
Skid Number Immediately After Resurfacing 
Coefficient for Rate of Change of Skid Number 

with Traffic Passages 
Final Value of Skid Number 

Default Percent Reduction for All Accidents 
Default Percent Reduction for Fatal and 

Injury Accidents 
Default Percent Reduction for Property- 
Damage-Only Accidents 
Default Percent Reduction for Head-On 

Accidents 
Default Percent Reduction for Rear-End 

Accidents 
Default Percent Reduction for Side-Swipe 

Accidents 
Default Percent Reduction for Right-Angle 

Accidents 
Default Percent Reduction for Left-Turn 

Accidents 
Default Percent Reduction for Parking- 
Related Accidents 
Default Percent Reduction for Fixed-Object 

Accidents 
Default Percent Reduction for Pedestrian 

Accidents 
Default Percent Reduction for Other 

Accidents 
Default Percent Reduction for Wet-Pavement 

Accidents 
Default Percent Reduction for Dry-Pavement 

Accidents 
Default Percent Reduction for Nighttime 

Accidents 
Default Percent Reduction for Daytime 

Accidents 



Symbol 


KM=2 


KM=3 


KM=28 


CCMA0(KM) 











CMA0M(KM) 











SD0R(KM) 


66 


43 


0a/ 


CSR(KM) 


-8.3 


2.428 


0a/ 


SDFR(KM) 


25 


70 


Qa/ 


DPRALL(KM) 








36 


DPRFI(KM) 








32 


DPRPD0(KM) 








38 


DPRH0(KM) 











DPRRE(KM) 











DPRSS(KM) 











DPRRA(KM) 











DPRLT(KM) 











DPRPR(KM) 











DPRF0 (KM) 











DPRPED(KM) 











DPR0TH(KM) 











DPRWET(KM) 











DPRDRY(KM) 











DPRNIT(KM) 








o. 


DPRDAY(KM) 












a/ The input value of SD0R(28) is shown as zero. This value is not used for 
geometric and traffic control countermeasures. The program will define 
SD0R(28) as equal to SD0R(2) because the current surface type, KWS, is 
2 for this example. The values for CSR(28) and SDFR(28) are treated in 
a similar manner. 



91 



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92 



C. Output Data for Example Problem 

Figure 9 illustrates the output data from the economic feasibility 
stage of the analysis. Three sets of benefit-cost calculations are shown. 
Each countermeasure is compared with the existing condition to determine if 
it is economically feasible. Each countermeasure was found to have a benefit/ 
cost ratio greater than one, and is, therefore, economically feasible. How- 
ever, the benefit/cost ratios for the three countermeasures are markedly 
different. Countermeasure 28, installation of warning signs, has the highest 
benefit/cost ratio, 79,86 ; countermeasure number 2, normal resurfacing, has 
the lowest benefit/cost ratio, 1.032. Because all three countermeasures have 
benefit/cost ratios greater than one, all three are included in the project 
formulation stage. 

The output from the project formulation stage is illustrated by 
Figure 10. First, the least expensive project, installation of warning signs, 
is compared with the next-to-least expensive project, normal resurfacing. A 
benefit/cost ratio of less than one resulted, indicating that installation 
of warning signs is more cost beneficial than normal resurfacing. The process 
was repeated to compare installation of warning signs with special resurfac- 
ing. Again, installation of warning signs was preferable. Therefore, the 
conclusion of the analysis is that installation of warning signs is the most 
appropriate countermeasure for this site, because both of the more expensive 
countermeasures have incremental benefit/cost ratios less than one. 

This conclusion and the cost and benefit data presented on the 
printouts should be considered by the state highway department, together 
with other available information, such as legal opinions, in making the final 
decision on which countermeasure to implement at this site. 



93 



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94 



XI. TESTS OF THE COMPUTERIZED MODEL 



Many of the basic concepts and relationships for the model were 
incorporated into the model before the results from Phase I were available. 
That initial logic and programming was tested by using simple analytical 
expressions for the subroutines that were not yet available. Ten cases were 
calculated manually and all the associated input and expected output were 
provided to FHWA's Data Systems Division. The 10 cases tested the features 
and options shown in Table 14. These preliminary tests demonstrated that the 
overall logic that controls the economic feasibility and project formulation 
stages operates properly. 

At the completion of Phase I, extensive logic was added to the 
program to incorporate the wet-pavement accident rate-skid number relation- 
ships and the changes of skid number with traffic wear. This new logic has 
been tested by FHWA using the example in Section X and found to operate pro- 
perly. 

There are a large number of logical branches within the program. 
The example problem tests only a limited number of these branches. A sys- 
tematic effort is needed to test every branch of the program to assure that 
all model capabilities are operating properly. Interested users should con- 
tact the FHWA Data Systems Division to determine the status of model testing. 



95 



TABLE 14 



FEATURES AND OPTIONS CHECKED IN PRELIMINARY TESTS 



Test No. 1 2 3 4 5 6 7 8 9 10 



Project Formulation 
Not Required 
Required 



x x 

xxxxxxxx 



Single Case Run 

With one variation 

With multiple variations 



xxxxxxxxx 



Multiple Case Run 



Applied Life 

Not specified in input 
Normal service life 
Terminated by resurface 
Terminated by rebuild 
Terminated by abandonment 

Specified in input 



X X X X X 
X 

X X X X 



X X X X 
X 



Final capital worth 

Not specified in input 
Normal salvage 

Possible recovery of service 
Leading to nor-nal salvage 
Leading to recovery of service value 
Specified in input 



X X X X X X 



xxxxxxxx 

X 



Period of Analysis 
Unequal lives 

Standard (long period) default 

Short period 
Equal lives 



xxxxxxxxxx 

X 



Prior Decision to Resurface 

Countermeasure involving resurface 
Countermeasure not involving resurface 



x x 

x x 



X 

X 



Right-of-Way Costs 
Nonzero Row cost 

Row Req. for fi 

Row not required for future rebuild 
Zero Row Cost 



96 



TABLE 14 (Concluded) 



Test No. 123456 789 10 



Capital Cost 
From file 
Read in input 



xxxxxxxxxx 

X 



ADT 



Calculated from coefficient 
Read in input 



Constant 



x x 



Cost Weight Factors 

Standard default values 
Non standard (read in) 



xxxxxxxxxx 

X 



Vestcharge (or Interest) Rate 
From file (.06) 
Read in input 



xxxxxxxxxx 



97 



XII. CONCLUSIONS 



This section deals solely with Phase II of the contract, the 
development of a benefit-cost model for wet-pavement accident reduction. 
As such, the conclusions concern the most important aspects of the model 
developed, rather than results of using the model, which is beyond the 
scope of the contract. 

1. An extremely broad and flexible benefit-cost model was 
devised, and specifications were provided to FHWA for program implementa- 
tion. 

2. The model, although originally envisioned for application 
in evaluating countermeasures to wet-pavement accidents, is sufficiently 
complete in logic and data to be applied to a far broader range of ac- 
cident types. 

3. The project developed an exceedingly comprehensive tabula- 
tion of countermeasures that have been applied or proposed as wet-pavement 
accident reduction techniques, and the model provides distinct logic and 
analysis techniques for the two classes of countermeasures--those that 
modify the skid number and those that do not. 

4. The model incorporates implicitly and explicitly the rela- 
tionships between accidents and skid number developed in this project, 
and it is unlikely that states would be able to assemble data sufficient 

to supercede these relationships, other than possibly to better definitize 
them for urban highways. 

5. Because the literature indicates that skid numbers and the 
changes of skid number with traffic and time are strongly dependent on local 
materials and practices, the model and support system permit users to supply 
values applicable to their area. 

6. The data collected in the project define relations between 
accidents and skid number for highway sections, but not for spot loca- 
tions, the model therefore treats spots as short, relatively high accident- 
rate locations with large skid number sensitivity. 

7. The model incorporates the best estimates of effectiveness 
currently available for geometric and traffic control countermeasures, 
although it is expected that many of these estimates are overly optimistic 
and perhaps should be revised if the user has what he believes to be more 
realistic estimates. 



93 



8. The model incorporates a unique and comprehensive treatment 
of user delay and fuel consumption costs associated with construction zones 
that should have broad applicability outside the confines of this study. 

9. The model is organized in anticipation that individual states 
will supply, via the support system data files, their own representative 

or average local values for expected lives, costs, and other characteristics 
of countermeasures, but it also anticipates that they may wish to use special 
or modified characteristics on occasions. 

10. The project included a thorough review and critical assembly 
of the driver behavior literature and its application to potential behavior 
modification countermeasures (especially speed control) to the wet-pavement 
accident problem. 



99 



XIII. RECOMMENDATIONS 



In a task of this sort, limited to the development of a tool, 
there are typically two types of recommendations — that the tool should be 
used, and that it can be improved. The development of the benefit-cost 
model for analyzing accident reduction countermeasures, is no different. 
Specifically, it is recommended that: 

1. The benefit-cost model be implemented and applied by several 
states or regions of states, initially as a means of gaining national ex- 
perience and confidence in its capabilities, and subsequently as a standard 
tool for providing highway administrators with benefit-cost data and com- 
parisons for use in their decisionmaking. 

2. The benefit-cost model be applied more universally than to 
just the special class of accidents that occur in association with wet pave- 
ment. 

3. Additional test cases need to be devised to more thoroughly 
test some logical branches of the program. 

4. Further data collection and analysis be conducted to better 
determine the role of skid number in accidents on urban facilities, but that 
until such determination, the relationships derived from the predominately 
rural data be utilized. 

5. Additional analyses, and perhaps data, be acquired relative 
to the role of skid number on accident rates at spot locations. 

6. The work reported relative to user costs associated with con- 
struction zones be expanded and applied as an element in overall construction 
and maintenance activity planning. 

7 The scope of the model be expanded by adding the capability 
to evaluate combinations of feasible countermeasures for simultaneous imple- 
mentation. 

8 9 The scope of the model be expanded by adding the capability 
to evaluate countermeasures that change the highway type, such as from two- 
lane to multilane. 

9. The model be expanded to incorporate a test of whether any 
known countermeasure could produce significant accident cost savings at a 
siven site. 



100 



1. Accident Facts , 1975 Edition, National Safety Council, Chicago, Illinois. 

2. Anderson, J. W. , and V. L. Pederson, "The Effect of Color in Guidance of 

Traffic at Interchanges," Investigation No. 318, Traffic Engineering 
Section, Minnesota Dept. of Highways, 1963. 

3. Arena, Philip J, Jr., "Expanded Clay Hot Mix Study," Final Report 

(Research Report No. 37), Research Project No. 65-3B, Louisiana HPR 
1(6), April 1969. 

4. Arizona Department of Highways, June 1963. 

5. Backlund, F. , "Detection Probability of Highway Traffic Signs," Paper 

presented at the Brussels Conference on Road Safety, Brussels, Belgium, 
January 7-10, 1969. 

6. Ballinger, C. A., "Automatic Icy Road Sign Study," Final Report, Research 

Unit, Planning and Research Division, Colorado Department of Highways, 
August 1966. 

7. Beaton, John L. , Ernest Zube, and John Skog, "Reduction of Accidents by 

Pavement Grooving," Highway Research Board Special Report No. 101 , 
pp. 110-119, 1969. 

8 Bezkorovainy, G. Ku. C. , "The Influence of Horizontal Curve Advisory 

Speed Limits on Spot-Speeds," Traffic Engineering , pp. 24-28, September 
1966. 

9. Blackburn, R. R. , W. D. Glauz, D. R. Kobett, and M. C. Sharp, "An Ice and 
Snow Detection and Warning System Feasibility Study," Contract FH-11- 
7428 (MRI Project 3394-E) , Midwest Research Institute Final Report, 
November 1971. 

10. Bleyl, R. L. , "Speed Profiles Approaching a Traffic Signal," Paper 

presented at HRB Annual Meeting, 1972. 

10a. Box, Paul C. , and Associates, "Traffic Control and Roadway Elements - 
Their Relationship to Highway Safety/Revised — Chapter 5, Driveways," 
Highway Users Federation for Safety and Mobility, 1970. 

11. Brackett, H. R. , "Flashing Beacons Used in Conjunction with Speed Reduc- 

tion Signing," Progress Report 1, Virginia Council of Highway Investi- 
gation and Research, Charlottesville, Virginia, February 1964. 

12. Brackett, H. R. , "Experimental Evaluation of Signing for Hazardous 

Driving Conditions," Progress Report 2, Virginia Council of Highway 
Investigations and Research, Charlottesville, Virginia, March 1965. 

101 



13. Brunner, Raymond J. , "Pavement Grooving, Final Report," Pennsylvania 

Dept. of Transportation Research Project No. 69-1, January 1973. 

14. Burg, A., and S. Hulbert, "Predicting the Effectiveness of Highway Signs," 

Highway Research Board Bulletin 324 , Washington, D.C., 1962. 

15. Burns, John C. , and Rowan J. Peters, "Surface Friction Study of Arizona 

Highways," Highway Research Record No. 471 , pp. 1-12, 1973. 

16. Cameron, C, and W. A. McGill, "A Comparative Evaluation of Speed Control 

Signs," Journal of the Australian Research Board , Vol. 3(8), pp. 3-11, 
1968. 

17. Conley, C. F. , and W. J. Roth, "Interchange Ramp, Color Delineations 

and Markings Study: Eratic Movements Survey Report," U.S. Department 
of Transportation, December 1967. 

18. Culp, T. B., and R. L. Dillhoff, "Watch for Ice on Bridge—Does it Reduce 

Accidents?" Ohio Department of Highways, Bureau of Traffic, October 
1970. 

19. Czar, M. , and D. Jacobs, "Centerline Marking Patterns," in Taylor et al. , 

Roadway Delineation Systems , NCHRP Report 130, 1973. 

20. Dahir, S. H. , W. E. Meyer, and R. R. Hegmon, "Laboratory and Field 

Investigation of Bituminous Pavement and Aggregate Polishing," 

Paper for presentation at Annual Meeting of the Transportation Board, 

January 1975. 

21. Dahir, S. H. , and W. G. Mullen, "Factors Influencing Aggregate Skid- 

Resistance Properties," Highway Research Record No. 376 , pp. 136-148, 
1971. 

22. David, R. E. , "Comparison of Delineation Treatments on a Two-Lane Rural 

Horizontal Curve," in Taylor et al., Roadway Delineation Systems , 
NCHRP Report No. 130, 1973. 

23. Eklund, K. , "The Conspicuity of Traffic Signs and Factors Affecting It," 

Reports from Talja , The Central Organization for Traffic Safety in 
Finland, Helsinki, Finland, 1968. 

24. Epps, Jon A., and Bob M. Gallaway, "Synthetic Aggregate Seal Coats - 

Current Texas Highway Department Practices," Texas Transportation 
Institute Research Report No. 83-1, May 1972. 

24a. Fee, J. A., "Interstate System Accident Research Study-1," U.S. Depart- 
ment of Transportation, 1970. 

102 



25. Ferguson, W. , and K. Cook, "Driver Awareness of Sign Colors and Shapes," 

Virginia Highway Research Council, Charlottesville, Virginia, December 
1966. 

26. Florence, Robert L. , and Herbert F. Southgate, "Experimental Sand-Asphalt 

Surface," Final Report, KYHPR-64-8; HPR-1(6), Part II, Kentucky Dept. 
of Highways, October 1970. 

27. Forbes, T. W. , "Driver Knowledge, Judgment and Responses in Causation 

and Control of Skidding," presented at the First International Skid 
Prevention Conference, Charlottesville, Virginia, 1958. 

28. Gallaway, Bob M. , and William J. Harper, "Final Report on the Use of 

Lightweight Aggregate in Flexible Pavements," Texas Transportation 
Institute Report No. 51-4, August 1967. 

29. Gallaway, Bob M. , and Jerry G. Rose, "Comparison of Highway Pavement 

Friction Measurements Taken in the Corner ing-Slip and Skid Modes," 
Highway Research Record No. 376 , pp. 107-122, 1971. 

30. Gillespie, T. D. , W. E. Meyer, and R. R. Hegmon, "Skid Resistance Testing 

From a Statistical Viewpoint," Highway Research Record 471 , pp. 38-45, 
1973. 

31. Glennon, John C. , "A Safety Evaluation of Current Design Criteria For 

Stopping Sight Distance," Highway Research Record 312 , pp. 33-54, 1970. 

32. Gwynn, D. W. , and J. Seifert, "Red Colored Pavement," Highway Research 

Record No. 221 , pp. 15-22, 1968. 

33. Hakkinen, S., "Perception of Highway Traffic Signs," The Central Organ- 

ization for Traffic Safety in Finland, Helsinki, Finland, 1965. 

34. Hammer, C. G. , "Evaluation of Minor Improvements, Part 6: Signs," 

California Division of Highways, for Department of Transportation, 
Washington, D.C., May 1968. 

35. Hankins, Kenneth D. , Richard B. Morgan, Bashar Ashkar, and Paul R. Tutt, 

"Influence of Vehicle and Pavement Factors on Wet-Pavement Accidents," 
Highway Research Record No. 376 , pp. 66-84, 1971. 

36. Hanscom, F. R. , "Driver Awareness of Highway Sites with High Skid Accident 

Potential," Final Report, BioTechnology , Inc., Falls Church, Virginia, 
July 1974. 

37. "Highway Safety Program Manual, Volume 13 - Traffic Engineering Services," 

U.S. Department of Transportation, Federal Highway Administration, 
Washington, D.C., 1972. 

103 



38. Hoffman, M. R. , "Evaluation of Traffic Lane-Use Control Signs," Michigan 

Department of State Highways, Report No. TSD-SS-112-69 , April 1969. 

39. Holmes, T. , and G. Lees, "A Combined Approach to the Optimisation of 

Tyre and Pavement Interaction," Wear , 20, pp. 241-276, 1972. 

40. Howard, A., "Traffic Sign Recognition," Proceedings of the Canadian Good 

Roads Association , October 1964. 

41. Ivey, Don L. , and Bob M. Gallaway, "Tire-Pavement Friction: A Vital 

Design Objective," Highway Research Record No. 471 , pp. 13-26, 1973. 

42. Jackman, W. T. , "Driver Obediance to Stop and Slow Signs," Highway Research 

Board Bulletin 161 , pp. 9-17, 1957. 

43. Jorgensen, Roy, and Associates, "Methods for Evaluating Highway Safety 

Improvements," NCHRP Report 162 , 1975. 

44. Jorgensen, Roy, and Associates, and Westat Research Analysts, Inc., 

"Evaluation of Criteria for Safety Improvements on the Highway," 
U.S. Department of Commerce, Bureau of Public Roads, 1966. 

45. Kassan, A. L. , and T. F. Crowder, "Improved Signal Visibility Reduces 

Accidents," Traffic Engineering , Vol. 19(7), pp. 42-44, 1969. 

46. Kummer, H. W. , and W. E. Meyer, "Tentative Skid Resistance Requirements 

for Main Rural Highways," NCHRP Report 37 , 1967. 

47. Lees, G. , and R. L. Sharif, "High Friction Dense Asphalts," Highways 

and Traffic Engineering , February 1971. 

43. Lees, G. , and A. R. Williams, "A Machine for Friction and Wear Testing 
of Pavement Surfacing Materials and Tyre Tread Compounds," Rubber 
Industry , Vol. 8, No. 3, June 1974. 

49. MacKenzie, Alex J., "Spray Grip Anti-Skid Surfacing Materials," Highway 

Research Record 376 , pp. 61-62, 1971. 

50. Missouri State Highway Commission, Research Report No. 69-10, December 

1969. 

51. Mullen, W. G. , S. H. M. Dahir, and 3. D. Barnes, "Two Laboratory Methods 

for Evaluating Skid-Resistance Properties of Aggregates," Highway 
Research Record No. 376 , pp. 123-135, 1971. 

52. Ottini, R. , "State Speed Limits and Their Relation to Safety," Proceedings 

of the Western Association of State Highway Officials , April 1956. 

104 



53. Please, A. , and D. R. Lamb, "Binder Properties and the Texture of 

Asphaltic Surfacings," Assoc, of Asphalt Paving Technology Proceedings, 
Vol. 40, pp. 324-353. 

54. Powers, L. D. , and H. L. Michael, "Effects on Speed and Accidents of 

Improved Delineation at Three Hazardous Locations," HRB Bulletin 300 , 
pp. 10-24, 1961. 

55. Ritchie, M. L. , "Choice of Speed in Driving Through Curves as a Function 

of Advisory Speed and Curve Signs," Human Factors , Vol. 14(6), pp. 533- 
538, 1972. 

56. Ritchie, M. L. , J. M. Howard, W. D. Myers, and S. Nataraj , "Further 

Experiments in Information Processing," Proceedings of 16th Annual 
Meeting of the Human Factors Society, Los Angeles, 1972. 

57. Rizenbergs, R. L. , J. L. Burchett, and C. T. Napier, "Skid Resistance 

of Pavements," ASTM Special Technical Publication No. 530, pp. 138-159, 
June 25-30, 1972. Also Interim Report KYHPR-64-24, HPR-1(8), Part II, 
Kentucky Department of Highways, July 1972. 

58. Rooney, Herbert A., and Thomas L. Shelly, "Thin Resinous and Aggregate 

Overlays on Portland Cement Concrete," California Division of Highways 
Research Report PWO 635121, June 1969. 

59. Rosenbaum, M. J. , P. Young, S. R. Byington, and W. Basham, "Speed Con- 

trol in Rural School Zones," Paper presented at 54th Annual Meeting 
of the Transportation Research Board, Washington, D.C., 1975. 

60. Rowan, N. J. , and C. J. Keese, "A Study of Factors Influencing Traffic 

Speeds," Texas Transportation Institute, College Station, Texas, 1961. 

61. Rutley, K. S. , "Control of Drivers' Speed by Means Other Than Enforcement," 

Ergonomics , Vol. 18(1), pp. 89-100, 1975. 

61a. St. John, A. D. , and D. R. Kobett, "Grade Effects on Traffic Flow 

Stability and Capacity," Final Report Draft on NCHRP 3-19, August 1974. 

62. Schwab, R. N. , "Minimize the Hazard of Restricted Visibility in Fog," 

HRB Special Report N143 , pp. 19-27, 1973. 

63. Sherman, George B. , "Grooving Pattern Studies in California," Hi ghway 

Research Record No. 376 , pp. 63-64, 1971. 

64. Stewart, C. F. , and A. Segueira, "Bridge Deck Frosting," California 

Division of Highways, Sacramento, November 1971. 



105 



65. Summala, H. , and R. N'a'atanen, "Perception of Highway Traffic Signs and 

Motivation," J. Safety Research , Vol. 6(4), pp. 150-154, 1974. 

66. Swilley, Harrison D. , Bob M. Gallaway, and Jon A. Epps , "Lightweight 

Hot-Mix, Cold-Laid Maintenance Mixture," Texas Transportation Institute 
Report No. 503- IF, December 1972. 

67. Taragin, A. , "Driver Performance on Horizontal Curves," Highway Research 

Board Proceedings , Vol. 33, pp. 446-466, Washington, D.C., 1954. 

68. Underwood, Jon P. , "Field Friction Performance of Several Experimental 

Test Sections," Texas Highway Department Report No. 126-1, March 1971. 

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crete Surface of a High-Speed Road," Road Research Laboratory Report 
LR 250, 1969. 

70. Wiley, C. , "Effect of Speed Limit Signs on Vehicular Speed," Department 

of Civil Engineering, University of Illinois, September 1, 1969. 

71. Williams, D. I., and M. D. van der Nest, "The Human Factor in Road 

Traffic Signs: The View of the Road User," Report No. CSIR PERS 113, 
Council for Scientific Industrial Research, Johannesburg, South Africa, 
May 1969. 

72. Williston, R. M. , "Effects of Pavement Edge Markings on Operator Behavior,' 

HRB Bulletin 266 , pp. 8-27, 1960. 

73. Winfrey, Robley, Economic Analysis for Highways , International Textbook 

Company, Scranton, Pennsylvania, 1969. 



L06 



APPENDIX A 



POTENTIAL SKIDD ING-ACCIDENT COUNTERMEASURES 

The skidding- accident problem is a long-standing one and a multi- 
tude of countermeasures have been attempted to alleviate the problem. The 
skidding-accident problem can be reduced by reducing the frictional demand, 
by increasing the friction supply of the pavement, or by reducing the acci- 
dent severity. Frictional demand can be reduced by either modifying the 
roadway geometry or by modifying driver behavior. An increase in frictional 
supply can be achieved by improved pavement design and improved tire design. 
Reduction of accident severity can be accomplished by constraining errant 
vehicles and by reducing obstacle hazards. 

A list of potential countermeasures was developed and submitted to 
the 16 cooperating state transportation and highway departments* for review 
and comments. Below is the list of possible countermeasures for reducing 
the skidding-accident rates. The comments and suggestions resulting from 
the states' review are incorporated in the list. The countermeasures are 
classified under the three major headings mentioned above. Tire design is 
outside the scope of the study and is omitted from the listing. 

Factors influencing driver behavior are extensive and involved. A 
complete description of the methods usable to influence driver behavior in 
controlling skidding is given in Appendix G. 



I . Reducing Frictional Demand 

A. Modifying Roadway Geometry 
1 . Curves 

a. Reduced curvature 

b. Reduce vertical curvature 

c. Increase superelevation 

d. Increase sight distance 



The cooperating states contacted were: California, Connecticut, Florida, 
Louisiana, Maine, Maryland, Massachusetts, Michigan, Mississippi, North 
Carolina, Ohio, Pennsylvania, Rhode Island, South Carolina, Washington, 
and West Virginia. 



107 



e. Install transition curves 



Remove ramp terminals and intersections on curves 



Eliminate broken back alignment 



Eliminate combinations of vertical and horizontal curves 



Increase cross slope on shoulders 



Stabilize and pave shoulders 



Widen shoulders 



Widen traveled way 



m. Relocate fixed objects 



2. Tangents 



a. Reduce grades 

b. Increase sight distance 

c. Increase access control 

d. Lengthen weaving sections 

e. Stabilize and pave shoulders 

f. Widen shoulder 

g. Increase cross slope 
h. Widen traveled way 

i. Relocate fixed objects 

j. Add climbing lane 

k. Close median openings 

1. Add raised median 



108 



3. Intersections 

a. Increase sight distance 

b. Reduce grades on approach 

c. Install left turn lanes on through highway 

(1) Using raised/curbed island 

(2) Using painted island 

d. Lengthen/install acceleration/deceleration lanes 

e. Eliminate at grade intersections 
£. Improve intersection alignment 

g. Eliminate surface water "ponding" areas 

B. Modifying Driver Behavior 

1. Wet weather speed limits 

2. Install safety lighting 

3. Install slippery when wet signing 

4. Install safe speed signing 

5. Install advance signing 

a. Caution 

b. Directional (including informational or motorists service) 

6. Install advance warning flashers 

7. Eliminate concentrated message areas 

8. Install overhead lane signs 

9. Delineation 



109 



a. Install striping 

(1) Edge and lane marking 

(2) Double-yellow median line 

(3) Painted median 

(4) Centerline striping at crests 

b. Install delineators 

c. Install markers 

(1) Ref lectorized raised pavement markers 

(2) Ref lectorized guide markers 

(3) Pavement rumble strips 

10. Install glare barriers 

11. Install intersection traffic control 

a. Stop signs 

b. Yield signs 

c. Flashing beacons 

d. Signals 

(1) For vehicles phase 

(2) For pedestrian phase 

e. Timing of signals 

f. Turn prohibitions 

g. Turn control 



110 



12. Improve driver licensing 

a. Driver education 

(1) Driver education in high schools 

(2) Adult driver education 

(3) Driver education of problem drivers 

(4) Wet-weather driver training 

b. Law enforcement 

(1) Selective enforcement 

(2) Increase number of highway patrolmen on the road 

(3) Vehicle inspection (annual and spot) 

c. Physical exams of drivers 

(1) Vision 

(2) Hearing 

(3) Reaction time 

II . Increasing Frictional Supply 
A. Selection of Aggregates 

1. Mineral hardness 

2. Acid-insolubility test 

3. Size 

4. Gradation 

5. Angularity 



111 



B. New PCC Pavement Finish 

1. Burlap drag 

a. Oscillating 

b. Not oscillating 

2 . Brooming 

3. Metal tines 

4. Roller with ridges 

5. Seeding with aggregate 

6. Coco matting 

7. Heavy belt 

a. Oscillating 

b. Not oscillating 

8. Wallpaper brush 

9. Wood float 
10. Wire drag 

C. New Bituminous Concrete Pavement 

1. Prevent glazing by too-early traffic 

2. Void content - prevent bleeding 

D . Maintenance 

1. Surface texturing 
a. Grooving 

(1) Longitudinal 

(2) Transverse 

112 



b. Etching 

(1) Muriatic acid 

(2) Hydrofluoric acid 

(3) Hydrochloric acid 

c. Abrading 

(1) Christensen concrete planer 

(2) Heater-planer 

(3) Weighted section of chain-link fence 

(4) Drum (with automatic punches for fracturing polished 

aggregate) 

(5) Shot and sandblasting 

d. Studs (on steel grid bridge decks) 
2. Overlays 

a. Plant mix seal (open graded) 

b. Bituminous chip-seal coat 

c. Rubberized sand asphalt mixture 

d. Synthetic resin mix 

e. Mastic asphalt concrete 

f. Epoxy resin seal coat 

g. Epoxy resin mortar 

III . Reducing Accident Severity 

A. Constrain errant vehicles 
1. Guardrails 



113 



2. Median Bariers 

3. Favorable side slopes 

B. Reduce Obstacle Hazards 

1. Eliminate obstacles 

2. Reduce obstacle severity 

a. Breakaway structures 

b. Guardrail diversion 

c. Impact attenuators 



114 



APPENDIX B 

SKID RESISTANCE CHANGE WITH TRAFFIC PASSAGES IN 
THE BENEFIT-COST MODEL 

The change in skid resistance during the life of a surface course 
can be important and needs to be incorporated in the benefit-cost model. 
With the current state of knowledge it appears necessary to forecast future 
skid numbers on the basis of local experience with specific aggregates in 
the climate of previous applications. 

The need to employ local experience rather than national research 
results is due to the complexities of both the tire-pavement interactions 
and the mineraology of aggregates employed. This appendix presents a brief 
overview of the tire-pavement interaction, the surface wear and polish pro- 
cesses, and the over generalizations that appeared in early publications. 
The appendix concludes by presenting the analytical form employed in the 
benefit-cost model to characterize the changes in skid number due to traf- 
fic. 

A more complete discussion of skid resistance is found in NCHRP 
Synthesis No. 14. 

Knowledge on how the skid resistance of surface courses changes 
during the useful life of the pavement is an important feature required by 
the benefit-cost model. This appendix discusses briefly the fundamentals 
associated with the skid resistance of the tire-pavement interface. This 
is followed by a discussion of the mechanisms involved in the skid resis- 
tance changes experienced during the useful lives of asphaltic concrete 
and portland cement concrete surface courses. Finally, a description is 
given of the analytical form used by the benefit-cost model to characterize 
the change of skid number in terms of total cumulative vehicle passages. 

1. Fundamentals of the Skid Resistance of the Tire-Pavement 
Interface : The braking and sidewise forces exerted on the tire by a pave- 
ment surface are thought to arise from three fundamental interactions. 
They are adhesion, hysteresis, and tearing or plowing. — > — 

The tire actually contacts the surface only at a few asperities. 
On a wet pavement the tire must squeeze out a local film of water in the 
vicinity of the asperity to make contact. The tire adheres to the asperity 
surface and a force is required to produce relative motion. 

When the tire moves with respect to the asperity the force required 
to deform the tire is not all recovered as the deformed area moves from the 
asperity. Consequently, to cause displacement a net force is required to 
overcome the hysteresis losses. Similar hysteresis contributions to braking 
and side forces arise from deforming the tire over larger features of the 
pavement surface, even though most of the areas involved may be separated 
by water or other attached films. 

115 



Microscopic examinations have been made of tire surfaces after 
slipping against pavement surfaces in laboratory tests. The examinations 
reveal that the tire is gouged or torn by microscopic asperities when they 
are high and sharp. The forces required to cause the permanent deformations 
also contribute to braking and sidewise forces exerted on the tire by the 
pavement. 

The microscopic asperities, their frequency, dimensions, and 
character are called the microtexture. The larger scaled variation in 
surface height, generally associated with small and large aggregate, is 
called the macrotexture. The macrotexture is in the true sense associated 
with the pavement surface. Microtexture is used to describe a pavement 
characteristic but is more correctly associated with individual pieces of 
aggregate. 

The macrotexture of the pavement surface is also important in 
providing escape channels for water under the tire footprint. When vehicle 
speed is increased there is a reduction in the time available for water 
to be forced from under the tire, and the water pressure then increases. 
If the passages formed by the macrotexture do not supply sufficient egress, 
water pressure will rise sufficiently to support the tire, and contact 
with the pavement will be reduced or eliminated. The extreme condition of 
no contact is called hydroplaning; negligible braking and sidewise forces 
can be transmitted in this condition. It is important to recognize that 
hydrodynamics can provide partial tire support which reduces the maximum 
magnitudes of braking and sidewise forces otherwise attainable. 

Consider again the three fundamental processes which provide 
braking and sidewise forces on the tire. The adhesion process does not 
require any relative motion between tire and pavement. The force contri- 
bution from hysteresis and gouging do require relative motion. The maximum 
braking force on a wet pavement is usually attained when the tire motion is 
a combination of rolling and slipping. The peak skid number is obtained 
under these conditions and is equal to the indicated friction coefficient 
times 100. The skid number generally in use is smaller and is obtained 
experimentally with a locked wheel; it is the coefficient of friction for 
that condition times 100. Most state highway departments employ locked- 
wheel test trailers and obtain data as skid numbers. A few states, and 
other countries, measure forces on a yawed tire (the Mu-meter) , which pro- 
vides a result which is frequently larger than the skid number but is not 
necessarily the peak skid number. 

2. Asphaltic Concrete Surface Courses : As the name implies, 
asphaltic concrete (AC) is a coalescence of mineral aggregate bound together 
by asphalt or mixtures of asphalt and other binder extenders. A large 
body of knowledge has been developed by investigators on the characteristics 
of AC and on emplacement practices. 2Q i 21 » 47 i 51 ) 5j ) 5 ^ A characteristic 

116 



of special interest here is the skid number provided during the life of 
the surface course. However, the cost, useful life, and structural proper- 
ties are also important characteristics. After examining the literature 
it appears that frequently generalizations have been deduced or suggested 
about the variation of skid number over the life of the pavement without 
regard for the complexities of the subject and without appreciation for 
the lack of scope in individual investigations. Unfortunately, there are 
few legitimate generalizations that can be broadly applied for the purpose 
of this project. This can be seen from the following description of the 
life of an asphaltic surface course, which was developed from pertinent 
findings of several investigators. 

When AC is mixed, prior to emplacement, the aggregate are coated 
with asphalt, which is rendered workable by one of three techniques. The 
asphalt may be heated (together with the aggregate), reduced (or cut) with 
volatile petroleum components, or processed as a water emulsion. The qual- 
ity and durability of the emplaced course depend on the ambient temperature, 
the surface temperature and preparation, the temperature or condition of 
the mix, the rolling schedule, and the post-emplacement protection from 
traffic. 

The grading of aggregates used can produce courses with a very 
small percentage of voids (close-graded), or with a large percentage of 
voids (open-graded). With the same type of aggregates and asphalt the close 
graded course has higher structural strength and is less subject to defor- 
mation or freeze damage. The open-graded course provides more drainage 
passages for water, and, in very high void designs, may actually provide a 
subsurface path for gross drainage to the pavement edges. 

When traffic first uses the surface, tires contact the asphalt 
coating which usually contains fines and possibly some small aggregate. 
For this initial wear-in period there are very little skid data and the 
skid number results are described variously as low or satisfactory. These 
results probably depend on the character of the fine and small aggregate 
and the initial macrotexture resulting from gradation and rolling. 

As wear due to traffic continues the asphalt is worn off the 
large aggregate and in many pavements the majority of actual contact occurs 
between the tires and large aggregate. 

The aggregate (of any size) that is contacted by tires is subject 
to wear and polish. Wear is the removal of surface material, and polish is 
the preferential removal of asperities so that their number and protuberance 
are diminshed. The wear and polish together with initial grading and 
asphaltic degradation determine the skid resistance in the early and sub- 
sequent life of the surface. 



117 



The exposed aggregate may previously have been polished by natural 
processes as in the case of river or glacial gravels. In this case the 
early skid numbers may be low and change little with time and traffic. If, 
however, the aggregates have been crushed or naturally have numerous asperi- 
ties, the early skid numbers may be high. The subsequent changes in skid 
number depend on several interacting factors. These factors and the ensuing 
progression of skid numbers are areas in which unwarranted generalizations 
have been advanced. 

From a practical standpoint there are two kinds of aggregate: 
those that wear and polish, and those that wear without becoming polished. 
However, there has been some confusion about these classes. 

Aggregate that wears and polishes may differ significantly in 
the rate at which polishing progresses. Generally, the soft minerals 
polish rapidly while the hard minerals polish slowly. The differences in 
polishing rates were first observed with practical consequences. The rapid 
polishing aggregate quickly became slick (contributing to low skid numbers), 
while in comparable time periods and traffic, the slow- polishing aggregates 
retained most of their initial skid number. As a result of these obser- 
vations there was a tendency to describe the slow-polishing aggregate as 
nonpolishing and the rapidly polishing aggregate as polishing or polish 
prone. There is, of course, a great practical difference between the rapid- 
and slow-polishing aggregate. In the case of the life history of a surface 
course, the rapid-polishing aggregates would, after a small number of traffic 
passages, deteriorate to a low skid number, while the slow-polishing aggre- 
gates might in the same service provide much higher skid numbers for time 
periods comensurate with the expected life of the surface course. Ultimately, 
investigators recognized that it is simply a matter of time and traffic 
differences: slow-polishing aggregate will finally polish and provide low 
skid numbers. This similarity may have been overemphasized in some cases 
where it could be inferred incorrectly that all aggregates polish. 

Nonpolishing aggregates can be subdivided into two types. In 
one type the mineral characteristics are essentially uniform and the non- 
polishing characteristic arises from the crystallography. Wear occurs with 
the removal of geometric elements that expose new micro surfaces with angu- 
larity and asperities. The aggregates that are manufactured by kilning 
shales and clays are of this type. The second type has nonhomogeneous 
mineral characteristics. Typically the rock will be a (naturally) cemented 
gritstone or sandstone. The angularity of the embedded sand or grit supplies 
the asperities. The individual embedded particles may polish but they have 
a limited life at the exposed surface because cementation fails due to wear 
or weathering. Consequently, new embedded particles are exposed and provide 
a renewal of unpolished surface. 



118 



The character of wear in the nonpolishing aggregate suggests 
that material may be removed in larger increments than for polishing aggre- 
gate. Some test data also indicate rather high wear rates. Consequently, 
the skid number should remain high with nonpolishing aggregate as long as 
they provide the major peaks in the macrotexture. However, there may be a 
long-term problem with wear and rutting. 

There are natural mineral aggregates with characteristics that 
suggest a range of polish susceptibility. Some soft mineral formations 
have inclusions of harder materials. It has been suggested that these 
aggregate have a minimum skid number that is superior to the skid number 
of aggregate composed of completely homogeneous minerals. Laboratory tests 
have shown that there is correlation (negative) between minimum coefficients 
and insoluable content. However, the correlation is not strong enough to 
make the test for insoluables a useable predictor for skid number. When a 
further classification is made as to shape and size of the insoluables 
their presence is strongly correlated with minimum skid number. 

The particulate debris formed by wear (detritus) have an effect 
on the rate of wear and polishing. Laboratory tests of slipping tires on 
pavement samples show that polish progresses at a faster rate when detritus 
are left in the wheel path. However, the minimum friction coefficient 
achieved with detritus present is larger than the coefficient that is reached 
when the pavement is flushed. The detritus in the tire-pavement interface 
remove asperities at a faster rate than does the clean tire. However, the 
detritus must generate some low order asperities in the process so that a 
higher polish can be achieved when the detritus are removed. 

The relative abundance and absence of detritus have been considered 
as one explanation for skid number variations that appear to be seasonal. 
The explanation is applicable if the exposed aggregate have been polished 
with detritus present close to the minimum achievable skid number. This 
would occur at the end of the "dry season". During the wet season additional 
polishing would occur when the detritus are repeatedly flushed from the road. 
At the end of the wet season a minimum skid number would be reached. And, 
during the ensuing dry season the detritus, left on the road, would produce 
wear and create a low level microtexture so that skid number should increase 
again. 

Field data have not been obtained with sufficient precision and in 
sufficient quantities to explain the detritus-season effects. It should 
be recognized that this seasonal effect would not be the same nationwide, 
because the patterns of precipitation differ from region to region. Factors 
in skid number measurement are also suspected of reflecting seasonal effects. 



119 






The skid numbers of asphaltic concrete surfaces are also influenced 
by other changes caused by time and traffic. The exposed surfaces of the 
asphalt are subject to chemical and physical change due to solar radiation, 
oxidation, and attack by contaminants in the atmosphere and surface water. 
As a result the asphalt is slowly lost from exposed surfaces. This may 
expose new fines and small aggregate that constitute part of the pavement 
surface in direct contact with the tire. The newly exposed aggregate have 
not been polished and may constitute a continually renewed source of effec- 
tive asperities. 

The atmospheric and surface water contaminants may also attack 
aggregate surfaces. No data were found on this subject but it appears 
likely that the chemical attack will be nonuniform due to small variations 
in the composition or crystallography within the individual pieces of aggre- 
gate. Thus, it is likely that in the absence of wear and polishing, some 
level of microtexture would be formed on exposed aggregate surfaces. 

The environmental attacks on the asphalt and on exposed aggregate 
surfaces appear to renew or form microtexture. It is important to recog- 
nize that these processes are in competition with polishing due to traffic. 

The skid resistance provided by an asphaltic concrete surface 
course during its useful life is seen to depend on numerous variables. 
They include: the asphalt characteristics, the mineral and crystallography 
of the aggregate, the initial state of the aggregate, the size grading of 
aggregate, the total vehicle passages and the traffic flow rates, the 
seasonal rainfall patterns, and possibly the atmospheric and surface water 
contaminants. 

For surface courses with polishing aggregate the usual history 
of skid numbers includes a relatively large initial value that depends on 
the initial condition of the aggregate. The skid number diminishes with 
vehicle passages. Some investigators find that the skid number stabilizes 
to a nearly constant value after a large number of vehicle passages. 
Other investigators find that the nearly constant final skid number has an 
inverse relation to the traffic flow rate. When the polishing and renewal 
processes are considered together with the variety of aggregates it seems 
likely that both findings may be correct. Consider first the case where 
a final, nearly constant skid number appears insensitive to traffic flow 
rates. The microtexture renewal processes in this case are simply too weak 
and slow to compete with any of the polishing processes caused by the range 
of traffic flows investigated. In contrast, the sensitivity to traffic 
flow rate indicates that microrenewal and polishing processes are in 
effective competition for the range of variables involved. 



120 



For surface courses with truly nonpolishing aggregate the history 
of skid resistance is very different from the cases with polishing aggre- 
gates. If all the large aggregate are nonpolishing it is likely that the 
skid number will increase with traffic usage. Some pavements exhibit skid 
number increases over long periods of time. Presumably the long-term 
increases are associated with wear that brings more of the nonpolishing 
surfaces into contact with tires. 

Since both the natural and manufactured nonpolishing aggregates 
are expensive, attention has been directed to mixtures of polishing and 
nonpolishing aggregates. Findings are not entirely consistent; however, 
it appears that for substantial benefits it is necessary to use the non- 
polishing variety for 507 o or more of the large aggregate. In these 
investigations it appears that insufficient attention has been paid to the 
relative wear rates of the polishing and nonpolishing aggregates used in 
combination. The relatively high wear rates of the nonpolishing aggregates 
may diminish their contacts with tires when mixtures of polishing and non- 
polishing aggregates are used. 

The skid resistance exhibited by an asphaltic concrete surface 
during its useful life is the result of several variables in complex inter- 
actions. The complexity has an impact on this study. Namely, it is not 
realistic to predict for nationwide application the skid resistance exhibi- 
ted by asphaltic concrete pavements during their useful lives. It is 
realistic to provide analytical forms with coefficients that can be assigned 
by individual state highway departments. The assignments can be based on 
the state experiences with their aggregates, emplacement practices, and 
climatic conditions. It will also be possible to supply coefficient values 
that will provide approximations when only the general character of the 
aggregate is known. 

Some seal and chip coats exhibit skid resistance characteristics 
similar to those of the asphaltic concrete. The polishing and nonpolishing 
characteristics of the chips have influences similar to those of the aggregate, 
The chip size and emplacement procedure sets initial macrotexture. Macro- 
texture diminishes with traffic due to wear and to the dis lodgement of 
aggregate. 

A very undesirable situation arises when a large part of the chips 
are lost by wear or dislodgement . The tire then contacts the seal material, 
which has poor macrotexture and most likely poor microtexture. 

Sand slurries are now used only infrequently. They have poor 
macrotexture but may have good microtexture associated with the sand particles 
Also, the microtexture may be renewed through the loss of exposed sand and 
the recession of the binder. 

121 



3. Portland Cement Concrete Surface Courses : PCC surface courses 
also exhibit skid resistance changes during their useful lives. These 
changes are discussed in terms of three pavement surface periods. In the 
first period, the initial texture (macrotexture) of the PCC surface is that 
formed in the plastic concrete, conventionally by brooming or burlap drags. 
The texture is formed in mortar that is composed of the cement with fine 
and some small aggregate. Early wear removes the cement from some of the 
fine and small aggregate. This, in combination .with areas of cement, supply 
the microtexture. The skid numbers in early life of PCC depend on the 
adequacy of the formed macrotexture and the microtextures of the fine and 
small aggregate. These aggregate may be subject to polishing, so that the 
skid number will be influenced by the relative rates of wear and polishing. 
Wear removes exposed aggregate and exposes previously unpolished particles. 
It is paradoxical that during this first period a poor cement (fast wearing) 
will tend to hold the skid number near to that maximum associated with the 
unpolished fine and small aggregate. This first period ends when wear 
reduces the macrotexture to a hazardously small value. 

The formed macrotexture may wear off before any larger aggregates 
are exposed. In the second period, a small macrotexture due to the small 
aggregates may persist for some time. The standard skid number measured at 
40 mph may not be alarmingly low during this period but heavy rainfalls, 
poor drainage, and high vehicle speeds may combine to produce high skid 
potentials from partial hydroplaning. 

A third period for the PCC surface begins when larger aggregate 
are exposed and create a larger macrotexture. The texture formed must 
depend on the relative wear rates of the large aggregate and the mortar. 
The polishing characteristics of large aggregate should have a pronounced 
effect on skid number during this third period. 

The skid resistance of PCC surfaces during their useful lives 
are influenced by a number of interacting variables. Again, it is not 
realistic to provide predictions of PCC skid numbers that will be useful 
nationwide. In the case of PCC it is even difficult to choose analytical 
forms that may have general utility. 

The conventional macrotexture formed by brooms or drags has in 
some cases been replaced by grooving. Grooves can be cut or ground into 
the cured pavement, or can be formed while the concrete is in the plastic 
state. Judging from the literature' ? 13,63/ ^ t a pp ea rs that most post-plastic 
state grooving has been performed on pavements in the second period (small 
macrotexture) in the attempt to reduce high wet-pavement accident rates. 
This remedial treatment appears to have been very effective, even though 
standard skid measurements do not indicate large increases in skid number. 



122 



For almost all the groove geometries used, an effective macro- 
texture is assured. However, the grooved pavement wears more rapidly than 
the same surface ungrooved. Initially the edges wear so that larger aggre- 
gate may be exposed there sooner than in an ungrooved pavement. When 
grooves are formed in the plastic state the presence of the groove macro- 
texture and the subsequent uneven wear should prevent the surface from 
attaining a second period character with small, ineffective macrotexture. 
The increased wear rates may also provide improved microtexture due to 
accelerated renewal and exposure. 

Some of the pavements that were first grooved (in a cured state) 
are now worn and the grooves in the wheel tracks virtually eliminated. It 
remains to be seen if the wear processes on the surface will perpetuate a 
satisfactory macrotexture. 

There is a safety aspect of grooving that has not been considered 
by investigators. Most grooves are visible or can be sensed from vehicle 
responses. As a result grooves may alert drivers and provide a safety 
benefit that is not associated with wet-pavement skid resistance. This con- 
cept is reinforced by the fact that a reduction in dry-pavement accident 
rates has followed grooving at some sites. 

4. Form of Skid Number Variations with Vehicle Passages : A review 
of the literature and a subsequent analysis indicated that a logarithmic 

form may be suitable to characterize the change of skid number with vehicle 

57/ 
passages. Following the work of Rizenbergs et al,— ' the form is 

SN = SN Q + C s In (C t x 10" 5 ) 

where 

SN = skid number, 

SN Q = initial skid number after a wear -in period, 
C = pavement coefficient, and 

Ct = total (accumulated) vehicle passages since the pavement surface 
was opened to traffic. 

This form does not account for the initial wear-in of asphaltic concrete, a 
period when the asphalt, the fines, and some small aggregate are worn off 
to expose the large aggregate. Outside of this limitation, the form has 
been shown — to be useful to describe the skid number of both standard 
asphaltic and portland cement concrete surface courses. The form with C_ 
positive may also be suitable for asphaltic courses made with manufactured 
aggregate. The general character of the curves for these nonpolishing 
surfaces indicates that the equation should be suitable; however, no 
numerical tests have been made. 



123 



The above form relating skid number changes with vehicle passages 
is incorporated in the benefit-cost model along with the following limits: 

1) C t x 10" 5 is replaced by 1.0 when C t x 10 "' is < 1.0, 

2) If C > 0, then SN has a maximum of SN^ (final SN for surface), 
and 

3) If C g < 0, then SN has a minimum of SN f 

All coefficients and limit values appear in the benefit-cost program as 
subscripted values applicable to a specific surface course. Specific values 
of the coefficients must be assigned by the individual state highway depart- 
ments using the model. The values of C g are best determined from least- 
square curve fits of state-collected pavement data. 



124 



APPENDIX C 

ACCIDENT COSTS 

Accident costs are changing rapidly. The costs of accidents are 
determined in the model from cost data published by the National Highway 
Traffic Safety Administration (NHTSA) and from several factors described 
below including the distribution of accident severities. While the distri- 
bution of accident severities is expected to be more stable over time than 
are accident costs, it is intended that both the accident cost and severity 
distributions used in the model should be updated at intervals commensurate 
with their rates of change. 

The following accident costs are incorporated in the model: 



Symbol Definition Cost 

CT1 Cost per vehicle involved in a property- $ 300 

damage-only accident 

CT2 Cost per injury 7,300 



CT3 



Cost per fatality 200,700 



These costs were obtained from "Societal Cost of Motor Vehicle Accidents, 
Preliminary Report," published by NHTSA in April 1972. The NHTSA cost for 
a fatality is higher than other available estimates, such as those published 
by the National Safety Council, primarily because the NHTSA costs include 
the value of future earnings lost due to an accident. The use of the NHTSA 
costs in benefit-cost evaluations by state and local governments has been 
recommended by the U.S. Department of Transportation in the Highway Safety 
Program Manual ,-iZ' and is therefore most appropriate fcr use in this model. 

It is recognized that users of the model may wish to modify the 
accident costs employed in a particular analysis. Therefore, the user may 
specify weight factors that modify the costs, as optional input to the 
model. These weight factors are identified below as FPD, FIA and FFA for 
property-damage-only, injury and fatal accidents, respectively, and have 
default values of 1.0. 

The average cost of a property-damage-only accident is: 

CA1 = (CT1) (FPD) (API) 

where CA1 = Average cost of a property-damage-only accident 

CT1 = Average cost per involved vehicle in property- 
damage-only accidents 

125 



FPD = Weight factor for property damage costs (default 
value = 1.0) 

API = Average number of vehicles involved in a property- 
damage-only accident 

In the same manner, the cost of an injury accident is: 

CA2 = (CT2) (FIA) (AP2) 
and the cost of a fatal accident is: 

CA3 = (CT3) (FFA) (AP3) 
where CA2 = Average cost of an injury accident 

CT2 = Average cost of an injury 

FIA = Weight factor for injury costs (default value = 1.0) 

AP2 = Average number of injured persons per injury accident 

CA3 = Average cost of a fatal accident 

CT3 = Average cost of a fatality 

FFA = Weight factor for fatality costs (default value = 1.0) 

AP3 = Average number of fatalities per fatal accident. 

In the analysis of each countermeasure , the model determines a 
weighted-average cost per accident for the accidents remaining after the 
countermeasure is implemented. This overall average cost is defined as: 

CAA = (CA1)(FA1) + (CA2)(FA2) + (CA3) (FA3) 

where CAA = Weighted-average cost of all accidents 

FA1 = Fraction of all accidents that involve property- 
damage-only 

FA2 = Fraction of all accidents that involve injuries 

FA3 = Fraction of all accidents that involve fatalities 



126 



Table 15 shows how AP2, AP3, FA1, FA2 and FA3 depend on area 
type and highway type. This table was assembled using data supplied by 
the States of California, Michigan and Washington for their entire state 
highway systems. The California and Washington data used are for the years 
1972 through 1975 and the Michigan data are for the years 1971 through 1974. 

The number of vehicles involved per property-damage-only accident 
(API) was reported as 1.71. No breakdown of API by area type and highway 
type is available. 

Table 16 illustrates the coefficients actually used in accident 
cost equations in the model. The table illustrates both the numerical value 
and the computer symbol used for each coefficient. 



127 



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II 



APPENDIX D 

ADDITIONAL USER COSTS DUE TO CONSTRUCTION 

This Appendix discusses the development of user costs associated 
with construction and maintenance activities associated with countermeasure 
implementation. The user cost factors that are given directly are travel 
time delay in vehicle-hours of delay per day and excess fuel consumed in 
gallons of fuel per day. Costs are determined from these factors by specify- 
ing the unit value of vehicle delays and the costs of fuel. 

This Appendix first summarizes the various formulas and values 
used for the determination of delays and fuel consumption, and then pre- 
sents the reasoning, assumptions and data used in developing the formulas. 

1. Summary : Five typical construction zone configurations are 
specified, based on the roadway type before construction and the number of 
lanes open during construction. The zone configurations considered are as 
follows : 

1. Two-way, two-lane roadway reduced to one lane with alternat- 

ing directions of traffic. 

2. Two unidirectional lanes reduced to one lane. 

3. Two-way, four-lane, divided highway reduced to two-way, two- 

lane. 

4. Three unidirectional lanes reduced to two lanes. 

5. Three unidirectional lanes reduced to one lane. 

Formulas for vehicle-hours of delay and excess fuel consumed were 
developed from curve fits for configurations 1 and 2 only. Data are pre- 
sented that could be used to develop formulas for the delay and fuel con- 
sumed for the other three configurations. 

Five area type-closure schedule combinations are considered for 
each zone configuration. These are shown in Table 17. The information 
necessary to develop formulas for other scheduling alternatives can be 
found in the following sections. 

a. Two- lane, two-way highway reduced to one lane 
(Configuration 1) : On a two- lane, two-way highway reduced to one lane 
with alternating directions of traffic the formulas for delay and excess 
fuel consumed are as follows! 



130 



Vehicle Hours of Delav 

D = [(C X A + C 2 A + C 3 A 3 )/(d + d x A)Jje 

where D = Vehicle-hours of delay per day, 

A = ADT/1,000 (both directions summed), and 

I = Length of one-lane section (miles). 

Table 18 provides the coefficient values. 



Code 

U-l 

U-2 

U-3 
R-l 
R-2 



TABLE 17 



AREA TYPE - CLOSURE SCHEDULE COMBINATIONS 



Area Type 
Urban 
Urban 

Urban 
Rural 
Rural 



Lane Closure Schedule 

Lanes closed 24 hr a day 

Lanes closed at all times except 6 to 
8 AM and 3 to 6 PM 

Lanes closed 8 AM to 3 PM 

Lanes closed 24 hr a day 

Lanes closed 8 AM to 4 PM 



TABLE 18 



COEFFICIENTS FOR DELAY EQUATION (Configuration 1) 



Area Closure Schedule 

Code Schedule 



i° ii 



_2 ^2 "3 

1055.23 -24.0705 -0.527063 23.0 -1.0 



Ci Co C* 
U-l All 24 hr 

U-2 6 to 8 AM and 3 to 6 PM 30.708 0.007222 0.038444 1.0 0.0 

U-3 8 AM to 3 PM 17.0173 -0.004555 0.026622 1.0 0.0 

R-l All 24 hr 1055.23 -24.0705 -0.527063 23.0 -1.0 

R-2 8 AM to 4 PM 24.650 0.508656 0.074933 1.0 0.0 



131 



Excess Fuel Consumed 

G = CjA + C 2 A 2 + C 3 A 3 + C-j-D 
where G = Excess gallons of fuel consumed per day, 

A = ADT/1,000 (both directions summed), 
C T = Average consumption at idle, gal/vehicle-hour , and 
D = Vehicle-hours of delay per day. 
Table 19 gives the coefficient values. 

TABLE 19 

COEFFICIENTS FOR EXCESS FUEL CONSUMPTION EQUATION (Configuration 1) 

Area Closure Schedule 

Code Closure C^ C2 C3 

U-l All 24 hr 22. 35-8. 5767 i *J -0.325+0.48907 i ^J -0. 007787 I $J 

U-2 6 to 8 AM and 3 to 6 PM 

Excluded 14.15-4.8047^ -0. 165+0. 164174 -0.000395i 

U-3 8 AM to 3 PM 7.70-2.9876^ -0. 100+0. 15609^ -0.002112i 

R-l All 24 hr 22.35-8.5767/ -0.325+0.4897^ -0.007787 { 

R-2 8 AM to 4 PM 7.70-2, 9876i -0. 100+0. 15609i -0.002112 i 



a/ The multiplier, I, is the length of the one-lane section (miles). 



The average fuel consumption at idle, Cj , is 0.376 gal/ 
vehicle-hour for the traffic composition including 107 o trucks. 

b. Two unidirectional lanes reduced to one unidirectional 
lane (Configuration 2) : On a highway with two unidirectional lanes reduced 
to one unidirectional lane, the formulas for delay and excess fuel consumed 
are as follows: 



132 



Vehicle Hours of Delay 

D = C Q + CjA + C 2 A 2 + C3A 3 
where D = Vehicle-hours of delay per day 

A = ADT/ 1,000 (ADT in the direction affected) 
Table 20 presents the coefficient values. 

Excess Fuel Consumed 

2 3 
G = C + CjA + C 2 A + C3A 

where G = Excess fuel consumed (gal Ions /day) 

A = ADT/ 1,000 (ADT in direction affected) 

Table 21 provides the coefficient values. 

2. Development of delay formulas for two-way two-lane highway 
reduced to one-lane with alternating traffic (Configuration 1) : In this 
configuration one direction of traffic is stopped while vehicles travel- 
ing in the opposite direction travel through the one-lane portion of the 
roadway. Figure 11 is a diagram of a typical work site of this configura- 
tion. Traffic control is normally accomplished by flagmen or signals at 
each of the stop lines. 

The operation of this type of zone, of course, is cyclic. A 
cycle of length T hours consists of four elements: 

T - t cl + t t + t c2 + t t 

where t , = Time for released vehicles to clear stop line 

cl 

(hours), direction 1 

t 2 = Time for released vehicles to clear stop line 
(hours), direction 2 

t = Time for last of released vehicles to travel the 
one-way section (hours) . 

The types of delays that a vehicle may experience in this zone 
configuration are: 

1. Stopped delays 

2. Delays due to reduced speeds 

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Length Vehicles are 
Restrained to One Lane 



rrm n ...... 1 1 1 1 1 



Wii i.n 1 1 1 I 1 hi 1 * 1 



Stop 



/ 



Work Area 



Stop Line 



Figure 11 - Two-Way , Two-Lane Highway Reduced to One Lane 

(Configuration 1) 

The computation of the delays is dependent on the mode of operation 
of the zone. The two modes of operation are saturated and unsaturated. The 
distinction between these two modes is addressed next. 

In general, the numbers of vehicles served during one cycle at 
saturation conditions are: 



n-, = t *R, and 
1 cl 

n 2 = t c2 *R 

ni = Number of direction 1 vehicles served in one cycle 
n2 = Number of direction 2 vehicles served in one cycle 
R = Approach flow rate (vph) at intersection capacity 
The total number of vehicles served per cycle is: 

n l + n 2 " R ^cl + t c2 ) ' 
(M + ^ " T " 2t f 



where 



But 



Therefore n x + n 2 = R(T - 2t t ). 

And, since there are if cycles per hour, the volume served (vph) during 
saturated conditions is: 



V 



, + V = R (1 - 2t t /T) vehicles/hour 

Clearly, the volume served is maximized by taking long cycles (large T) . 
However, an upper limit on acceptable cycle length for drivers is about 5 min 
or 1/12 hr. This value is taken as the condition separating two modes of 
operation. This should reduce delay under those conditions. For demand 
volumes, Vj + V 2 , above R [1 - 2t t / (1/ 12)] , the facility is saturated or 
oversaturated, and the cycle time T , of 1/12 hr will result in queues that 
will grow at each of the two approaches. For demand volumes less than that 
value the cycle period will be set by the demand. 



136 



When the cycle period, T , is set by the demand, the period t c 
is sufficient to exhaust the queue in each direction. 



Thus, 



t cl = VjT/R, and 
t c2 = V 2 T/R. 



th 



This simply states that the time required for the i n direction vehicles to 
clear the stop line is sufficient to clear all vehicles that arrive in one 
cycle. Then, since 

T = fc cl + t c2 + 2t t = (V 1 + V 2> T/ ( R > + 2t t> 
2t fc 



T = 



1 - 



v i + v : 



This equation gives the desired cycle period under unsaturated conditions. 

a. Delays due to stopping : We first consider the unsaturated 
case. For direction 1 the stopped delays during a cycle start when the period 
t c ^ ends. We count time from that origin in the following development. 
Vehicles arrive at the rate Vi per hour and are stopped. The first vehicle 
to arrive and be stopped is released after time (t c 2 + 2 t t ) . The last 
vehicle stopped in direction 1 crosses the stop line at time (t_o + 2t t ) + 
(t c 2 + 2t t )*V\R, where the second term accounts for clearing time required 
for vehicles in the stopped queue after the first vehicle in the queue has 
been released. Note that some of the vehicles will not be forced to stop. 
The number of direction 1 vehicles per cycle that do not need to stop is 



V l^cl " (t c2 " f 2t t>V R ] ■ 

Assuming constant arrival rates, the stopped delay per cycle 
in direction 1 is approximated as 



1/2 



< fc c2 + 2t t )(1 + ¥ 



The stopped delay time per cycle in direction 2 is obtained 
by substituting subscript 2 for 1 and vice versa. Then, the sum of the 
stopped delays in both directions is 

I v l 2 

Stopped delay per cycle = 1/2 I (t c 9 + 2t t )(l + — ) 



+ 1/2 



(t cl ,+ 2t t )(l + ^) V 2 



137 



Eliminating t^, t « , and t using the previously developed expressions 
gives 



Stopped delay per cycle = 



T^Vxfa^rKi-^) 



^2 



+ V- 



V?. 



a-^Xi-hr) 



2 



Dividing this expression by T , the time per cycle, gives the delay ex- 
pressed as vehicle-hours per hour. (This expression is applicable only 
for unsaturated flows.) 

The value of R , the intersection capacity, was taken as 
(1300) (1.30) s=» 1700 vph, where 1300 is an approximation for several geo- 
metries applicable to construction zones and the factor, 1.3, adjusts for 
no turns. Moreover, t t can be expressed as the quotient of the length 
of the one-way section (miles) and the speed of vehicles on a one-way sec- 
tion (mph). The program uses 30 mph as this speed. 



V = Vj_ + v 2 
case where 



The above expression can be further simplified. Let 
the total of the two approach volumes. For the special 



Vx - v 2 , 



Stopped delay = ? 



VL(1-— )(!+—) J 



2R' 



2R' 



veh ic le-hour s /hour 



This represents a "worst case" as can be verified by examination of situa- 
tions where V^ £ V 2 . This is the case used in subsequent developments 
for unsaturated flows . 

When vehicles arrive at a greater rate than can be served 
during the cycle, a queue forms. Under these conditions we treat the total 
queue in two parts. One is the queue to be served during the cycle, the 
served queue. The second is the wait queue—vehicles that must wait through 
one or more cycles. 

The number of vehicles in the wait queue is the excess of 
arrivals over the number served at the saturation rate since oversatura- 
tion began. The number of such vehicles at any time, t , is 



w 



(t) = | [V( T ) - V s ]di 



where 



V(t) = Demand volume as function of time, 



138 



V = Saturation flow rate, and 
s 



t = Time when oversaturation began. 
o 

The stopped (or creeping) delay in the wait queue is 

t 



D w (t) = I N (t)dt vehicle -hours, 



where the integral is evaluated over all times when N (t) s 0. The total 
stopped delay accumulated during oversaturation is 



D(t) = J [D rs + N w (t)]dt 



where 



D rs = Rate (vehicle-hours/hour) that stopped delay is incurred 

in the served queue with saturated flows (T = 0.0833 hr) , 
(Note that D rs = R(l-24t t ).) 

b. Delay due to reduced speed : The reduced speed is 30 mph; 



2000 



otherwise the speed in rural areas would be U = (50 
V = total of the two-way demands (vph). 

This delay per vehicle is ^(twT - — ) 

where I = length of one-way section (miles). 

The total delay per hour due to reduced speed = Vif— - — j 
Table 22 gives reduced speed delay factors for given demands. 



V) mph, where 



TABLE 22 
REDUCED SPEED PET .AY FACTORS 





Normal 


Volume 


Speed 


V (vph) 


U (mph) 





50 


200 


48 


400 


46 


800 


42 


1200 


38 


1600 


34 


1800 


32 


1900 


31 


2000 


30 



Delay /Mile 

/ Vehicle-Hours \ 
\ Hour Mile / 



2.5 

4.636 

7.616 

8.424 

6.272 

3.749 

2.043 





139 



c Total delay data : Using the delay equation developed 
for unsaturated conditions the two -direction sum of stopped delays was com- 
puted. This equation was used to compute delays at all volumes, since the 
definition of saturated conditions depends on travel time, t t , and thus 
the length of the work site. If the volumes shown represent saturated or 
oversaturated conditions, the delays will of course be underestimated. 

The computed values are plotted in Figures 12 and 13. 
In Figure 12 the values of delay due to reduced speeds were also added 
and the total is shown as a dashed curve. This latter delay was found to 
be important at volumes up to 1400 vehicles per hour, and is not in- 
cluded in Figure 12, which covers volumes of 1400 to 1700. The bottom 
curve is used for volumes of 1400 to 1620 and the top curve for volumes 
from 1630 to 1700. 

The Highway Capacity Manual gives a breakdown of the average 
fraction of the ADT that can be expected during each hour of the day (Figure 
3.6, p. 32). With this breakdown and the information from Figures D-2 and 
D-3 we can determine the daily delay for rural or urban conditions under a 
number of construction schedules. 

Figure 14 gives the computed delay versus ADT for schedule 
R-l (lane closed 24 hr per day) or R-2 (lane closed 8 AM to 4 FM) . Also 
shown are equations developed by curve fitting. 

Figure 15 gives the delay versus ADT under schedules U-l 
(lane closed 24 hr per day), U-2 (lane closed all hours except 6 to 8 AM 
and 3 to 6 FM) , and U-3 (lane closed 8 AM to 3 PM) . Again, equations de- 
veloped by curve fitting are given. 

3. Development of delay formulas for multilane highways : Several 
construction zone configurations are commonly used on multilane highways. 
Four configurations considered here are shown in Figure 16. 

The vehicle-hours of delay in multilane construction zones arise 
from reduced speed and queuing. When queuing occurs, delays result from 
the stopped delay of vehicles and the reduced speed that the vehicles travel 
when going through the zone. 

a. Reduced speeds : When capacity is not exceeded the delays 
are due entirely to reduced speeds. Let E be the delay vehicle-hours/ 
hour) due to reduced speeds. 



E = i(JL - -±-) 

u r u n 



i u 

a r n 

where I = Construction zone length (miles) + 0.20 

u r = Reduced speed in zone, and 

140 



200 



100 



With Reduced Speed 
Delay Added 



10 




Note: Multiply the Ordinate 
Values by the Length of the 
One-Lane Section, JL , (Miles) 
to Obtain Stopped (+ Reduced 
Speed) Delays in Vehicle 
Hours/ Hour 



J. 



Figure 12 



4 6 8 10 1 

Total Demand (Both Ways Summed), (100 vph) 

Stopped Delays, Configuration 1 for Volumes up to 
1,400 vph 



14 



141 



10.000 



1640 



1650 



1660 



1670 



1680 



1690 



o 



4> 

> 



1,000 — 



100 



Abscissa Scale 
is at Too 



Note: Multiply the Ordinate 
Values by the Length of the 
One- Way Section, 2 , (Miles) 
to Obtain Stopoed Deiays in 
Vehicle Hours/ Hour 



Abscissa Scale 
is at 3ortom 



14 



.2 .4 .6 .8 



15 - 2 A - 6 - 8 16 



Total Demand (3oth A'ays Summed), (100 vph) 



.2 .4 



Figure 13 - Stopped Delays, Configuration 1 for Volumes of 
1,400 to 1,700 vph 



142 



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143 



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144 







Teiicorar\ 




Stnptng 


KEY 




=» Tvoe 111 


Barricade 


■^ Type l 


Barricade 


l Cones 





Two Unidirectional Lanes 

Reduced to One Lane 

(Configuration 2) 



Two-way Four Lane Divided Highway 

Reduced to Two-way Two Lane 

(Configuration 3) 



Figure 16 - Multilane Construction Zone Configurations 



145 



Direction 
of Travel 



X [- - - - 1 - -I-,- 



tTTifrr 



te 



A 



Three Unidirectional Lanes Reduced to Two Lane 
(Configuration 4) 



Direction 
of Travel 



I 1 IMIM1MI 



►f* 



Note: 

L = Minimum length 

of taper 
S = Numerical value 

of the speed limit 

or 85 percentile 

speed 
W = Width of offset 



k 



L=SxW2L L = SxW 



Key: 

I — I Type I Barricade 
A Cone 



Three Unidirectional Lanes Reduced to One Lane 
(Configuration 5) 

Figure 16 (concluded) 



146 



u = Normal speed in zone. 

The value, 0.20, is used as the average length of the taper, and u and 
u n depend on the volume, V , which is less than capacity. 

Figure 17 shows the speeds of vehicles in the various configura- 
tions and during normal roadway operation. During the time queues are 
present u will depend on demand volume but u will be 30 mph for 
capacity flow conditions in the construction zone. Thus, the delay from 
reduced speeds when a queue is present is E = £(1/30 - 1/u ) . 

Using the above formula and the general data on hourly volumes 
and vehicle population given earlier, a representation of the delay in 
two unidirectional lanes reduced to one lane (configuration 2) was devel- 
oped. The process used may be explained easily by an example. Referring 
to curve 1 in Figure 17, the normal average speed u^ in a zone at one- 
eighth of capacity (0.125) would be 55 mph. Using curve 3 in Figure 17, 
the reduced average speed u r would be 50. The last two columns of 
Table 23 gives the results of calculations of delays, with and without 
queue dissipation, for various volumes. A plot of the information in 
Table 23 is shown in Figure 18. 

Figure 18 and the traffic demands in 1-hr periods of a day 
(from the Highway Capacity Manual ) were then used to develop the hourly 
vehicle delays experienced in each mile of a construction zone due to 
reduced speeds. Figure 19 is a plot of this information for schedules 
U-l, U-2 and U-3 (see Table 17). 

In Figure 19 the coefficients are given for the best fit for 
each of the curves. These three curves represent the total delay for all 
times except when there are queues present. For example, on the U-l curve 
the ADT where queues could be expected during some hours of the day (V > 
2,000) is 23,000. This means that, for the U-l schedule, stopped delay must 
be added for ADT's greater than 23,000. Thus, the U-l coefficients shown 
can be used for ADT's £ 23,000. For the U-2 and U-3 curves, queues can be 
expected for ADT's of 35,000 and above. 

b. Stopped delays : When queues are present, delays from 
stoppage in queues must be added to reduced speeds during queue dissipation, 
The computed values for these additional delays are shown in Table 2 4. 
The value for stopped delays (AD^) was computed for each hour that queues 
are present from the formula: 

(*t) 2 

*°wi - N io < At > + < V i " V s)™2- . 



147 



c c 

o> c g 

c « £ o 

o c q -2 

-I o - 




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o 




fl 

4J 
iH 

o 

fa 


n. 






• 




01 


o 




c 

cfl 
tH 
t-4 

4J 




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3 


>o 


tz. 


s 




o 




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D 


A 




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A 




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c 
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• 


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i-4 




u- 


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148 









TABLE 23 
















DELAYS FROM 


REDUCED SPEEDS 


(CONFIGURATION 


2) 


De 














lay During 










Delay 




Queue Dissipation 


Fraction 




Reduced 


Normal 


(-L-i)v 




(■ 


1 1 \ 
) v 

u r u n / 


of Normal 


Volume 


Speed 


Speed 


/Vehicle-Hours 
\ Hour Mile 


■) 




With 


Capacity 


V (vph) 


U r (mph) 


U n (mph) 




U n = 30 








50 


55 












0.125 


500 


50 


55 


0.9091 






7.576 


0.200 


800 


46 


55 


2.8458 






12.121 


0.300 


1200 


40.6 


54.4 


7.4978 






17.941 


0.400 


1600 


35.3 


53.3 


15.3070 






23.315 


0.500 


2000 


30.0 


51.6 


27.9070 




^ 






0.600 


2400 


30.0 


49.3 


31.3186 










0.700 


2800 


30.0 


46.4 


32.9885 








Queue is not 


0.800 


3200 


30.0 


43.3 


32.7635 








dissipating 


0.900 


3600 


30.0 


39.9 


29.7745 






► 


for these 


0.950 


3800 


30.0 


38.0 


26.6665 






volumes . 


0.980 


3920 


30.0 


36.0 


21.7780 










0.990 


3960 


30.0 


34.8 


18.2069 










1.000 


4000 


30.0 


30.0 







> 







Notes: Capacity flow, V s , taken as 2000 vph. 

For V > 2000 vph, queue will increase. 

After queue is normal but V < 2000 vph, U n will remain at 
queue dissipates. 



iph until 



149 




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0) 


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CN 








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3 


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f 


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Q 



14-1 

o c 
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CO i-l 

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3 « 

!- 
J= 3 

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J= CJ 

CD w 

> 



oo 



0) 

>-. 

3 
60 



00 



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(a|!W jnoH)/XD|3Q sjno(-| -i\b/\ 



150 



420 
400 
380 
360 
340 

320 - 



Coefficients 



_4) 


300 


2 




o 


280 


Q 








\ 






260 


3 









X 




_c 


240 


> 




"O 


220 


0) 




0) 




n 




00 


200 


■D 




ID 




O 




■u 


180 


<D 




Oi. 




o 


160 


<W 




D 




Q 


140 


>. 




D 




(1) 
Q 


120 



100 
80 
60 
40 
20 



OLA, 




Schedule ' 

U-l -0.392756 0.239301 0.003488 

U-2 0.147750 0.073776 0.002554 

U-3 0.137668 0.038042 0.001949 



= C]A + C 2 A 2 + C3A 3 



Veh Hours 
Day Mile 

Where A = (ADT/1000) in Direction Affected 



Note: U-l schedule is prohibitive 
beyond A = 30 because of large 
delays in queues. 




ADT/1000 ( In Direction Affected) 



Figure 19 - Delays Due to Reduced Speeds, Configuration 2, Urban 



151 



TABLE 2 4 

delay: due to stoppage in queues and reduced speeds durini 







QUEUE 


DISSIPATION FOR CONFIGURATION 2 




Demand 




Stopped Delay in Delay Due to Reduced Speeds 




Hour Volume 


Queues AD During Queue Dissipation 


Hour 


(vehicle /hour) 
28,000 (U-l) (Note 


(vehicle-hour) (vehicle -hour /mile) 


ADT = 


, effect on U-l starts at 23,000 ADT.) 


7-8 


2,128 




64.0 


8-9 


1,568 




18.96 2.52 


15-16 


2,156 




78.0 


16-17 


2,436 




374.0 


17-18 


2,156 




670.0 


18-19 


1,484 




490.0 9.30 


19-20 


1,344 




41.02 3.54 
1,735.98 15.36 


ADT = 


33,000 (U-l) 






7-8 


2,508 




254.0 


8-9 


1,848 




432.0 3.95 


9-10 


1,485 




123.04 6.36 


15-16 


2,541 




270.5 


16-17 


2,871 




976.5 


17-18 


2,541 




1,669.0 


18-19 


1,749 




1,827.5 5.90 


19-20 


1,584 




1,494.0 8.30 


20-21 


1,287 




929.5 10.20 


21-22 


1,221 




210.74 7.69 
8,186.78 42.^0 


ADT = 


38,000 (U-3) 


(Note 


, effect on U-2 and U-3 starts at 35,090 ADT.) 


8-9 


2,128 




64 


9-10 


1,710 




28.25 2.93 


14-15 


2,166 




83.0 


15-16 


2,926 




12.83 1.95 
188.08 4.88 


ADT = 


38,000 (U-2 > 


= U-3 


from above, plus.) 


18-19 


2,014 




7.00 


19-20 


1,824 




0.56 0.37 



195.64 5.25 



152 



where N. = Number of queued vehicles at the beginning of the 

i*-" time intervals, 

At = Duration of time interval (hours), 

V. = Demand (vph) during i time interval, and 



Moreover 



V s = Saturation (or capacity) flow (vph). 

N io = N (i-l)o + (V i~l " V s>( At )» and 
N (i-hl)o " N io + < V i " V 8 )(At) 
During the interval that the queue dissipates, 



At=^ 



V - V- 
v s v i 



and the stopped delay during that interval is: 

N. (At) + (V - V ) W~ - (Nlo)2 
M LO (At) + (V. V s ) 2 - 2(Vg _ v ^ 

The reduced speeds during the queue dissipation (AR* /.) 
are computed exactly as the delays due to reduced speeds except that u r 
is always equal to 30 mph. 

Approximating the values of AD^ with a quadratic leads 
to the following forms: 



U-l: AD T7 , = 39675 - 3450A + 75A 2 ; A > 23, 

U-2: AD wi = 28175 - 1610A + 23A 2 ; A > 35, and 

U-3: Al^i = 52307 - 2989A + 42. 7A 2 ; A > 35 
where 

A = ADT/1000 

Formulas for the R-l and R-2 schedules can be approximated by using the U-l 
coefficients for R-l schedule and the U-3 coefficients for the R-2 schedule. 

The addition of the formulas for stopped delay and the formu- 
las for delay due to reduced speed result in the following form that approxi- 
mates the total delay D: 



153 



2 3 

where D = C Q + CjA + C 2 A + C^A 

D = Vehicle-hours of delay per day, and 

A = ADT/1000 (ADT in the direction affected). 

These are the coefficients given in Table 21. 

4. Development of formulas for excess fuel consumption : Fuel 
costs are the major component of increased operating expense and are the 
only costs treated here. Fuel costs can be affected by up to three factors. 
The first is a speed change cycle from the normal speed to a stop and back 
to normal speed. (This is applied for each vehicle although some will not 
need to stop.) The second is fuel consumed during idling while in the 
stopped delay. The third is the fuel consumed in traversing the construction 
zone minus the fuel that would have been used at normal speed. Note that the 
contributions of the individual factors may be negative. 

In order to compute the excess amount of fuel consumed for various 
conditions, it was necessary to specify the percentage of passenger cars and 
trucks in the vehicle population. The specified vehicle population is 90% - 
passenger cars, 1% - 5,000 lb delivery trucks, 2% - 12,000 lb single unit 
trucks, and 1% - 40,000 lb gasoline-powered semitrailers or 50,000 lb diesel- 
powered semitrailers. 

a. Excess fuel consumption formula for two-lane, two-way 
highway reduced to one-lane of alternating traffic : Table 25 presents data 
needed to compute the excess fuel consumption due to speed change cycles and 
due to reduced speeds. Information in this table and the hourly volume data 
referenced earlier were used to compute the excess fuel consumed, plotted in 
Figure 20. 

The fuel consumption due to stopped delay is 0.376 gal. for 
every vehicle hour of stopped delay. 

By combining equations that approximate the curves for excess 
fuel consumption due to speed change cycles and reduced speed plus the rela- 
tionship for fuel consumption due to stopped delay we can determine the 
following formula for excess fuel consumed: 

2 3 
G = C-jA + C 2 A + C 3 A + CjD 

where 

G = Excess gallons of fuel consumed per day, 

A = ADT/ 1,000 (both directions summed), 

C T = Average consumption at idle, gallons/vehicle hour, and 

D = Vehicle hours of delay per day. 
154 




o 
o 

X 

LU 



8 10 12 
ADT/1000 



14 



20 



Figure 20 - Excess Fuel Consumption, C 



onf iguration 1, Urban 



155 



-50 r- 



o 



D 
O 

-o 
<d 
<u 

Q. 
CO 

■a 

a» 

Q 

3 

V 



D 

Q 

"D 

0) 

£ 

3 

c 

o 

U 



0) 

3 
Li_ 



-40 - 



-30 - 



«. -10 




6 8 10 12 

ADT/1000 



Figure 20 (concluded) 



156 



Vo lume 


Normal Speed 


V (vph) 


U n 


(mph) 







50 


200 




48 


400 




46 


800 




42 


1,200 




38 


1,600 




34 


1,800 




32 


2,000 




30 








-1. 


38 


-2. 


16 


-2. 


40 


-1. 


56 


-0. 


32 













TABLE 25 

EXCESS FUEL CONSUMPTION, CONFIGURATION 1 

Excess Consumption Excess Consumption 
Due to Speed Change Cycles Due to Reduced Speed 
(gal/hr) (gal/hr-mile) 



4.26 

8.00 
14.08 
18.36 
21.12 
21.78 
22.20 



Table D-3 gives the coefficient values. 

b. Excess fuel consumption formula for two unidirectional 
lanes reduced to one unidirectional lane (Configuration 2) : On multilane 
highways during periods when there is no queuing added fuel consumption 
arises from only two sources, a speed change cycle between the normal and 
reduced speed, and traversing the zone at a reduced speed. When queues are 
formed or are dissipating, all three factors are involved: a speed cycle 
from normal speed to stop and then back to normal; a lower than normal 
speed in the zone of 30 mph; and the fuel consumed during idling for the 
vehicle hours in queue. (Actually, the time in queues is spent at inter- 
mittant speeds less than 30 mph. This is a much higher fuel consumption 
condition than would occur during normal travel through the queue length. 
We approximate the difference by the idle consumption during time in the 
queue. ) 

Figure 21 gives the excess fuel consumption due to speed 
change cycles. The dashed line includes the excess fuel consumed when 
queues formed in previous hours are being dissipated. Figure 22 gives 
the excess fuel consumption due to reduced speeds. During queue dissipa- 
tion the reduced speed, u r , is always equal to 30 mph. This effect is 
accounted for in the dashed line in Figure 22. 

The information shown in Figures 21 and 22 was used along 
with the hourly volume breakdown in the Highway Capacity Manual to compute 
the data shown in Figure 23. Equations were determined that approximate 
each of the curves shown. (The equations are given in Figure 2 3.) 



157 



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Figure 2 3 - Excess Fuel Consumed, Configuration 2 



160 



To obtain the total excess fuel consumed, the two equations 
for each schedule that are given in Figure D-13 are combined. Also, when 
queues are present the fuel consumed idling for the vehicle-hours in queue 
must also be added. The vehicle-hours in queue were determined as part of 
the delay computation for this configuration (Section D.3.b). This figure 
was combined with the two previous equations for each schedule to give the 
excess fuel consumed for two unidirectional lanes reduced to one lane. 
The equation is: 

2 3 
G = C Q + C-|A + C 2 A + C3A 

where 

G = Excess fuel consumed (gallons/day), and 

A = ADT/ 1,000 (ADT in direction affected) 

Table D-5 provides the coefficient values. 



161 



APPENDIX E 

FLOW DIAGRAMS AND SPECIFICATIONS FOR 
BENEFIT-COST PROGRAM 

This appendix presents the flow diagrams and specifications used 
to program the benefit-cost model. The overall benefit-cost flow diagram, 
presented as Figure 3 in the text, is repeated here to place the following 
discussion in context. Then, the flow diagrams for each subroutine in the 
program are individually presented and discussed. 



A. Benefit-Cost Flow Diagram 

The benefit-cost flow diagram is shown in Figure 2 4. The notes 
on the figure explain the nature of the computations executed at each stage 
of the analysis. One pass through the logic diagrammed in the figure com- 
pletes the benefit-cost analyses of all requested countermeasures at one 
highway site or section. Until the call to subroutine EFEAS each routine 
deals with one aspect of each counter-measure requested. In EFEAS and PFRM 
each requested and feasible countermeasure is evaluated for its benefit/ 
cost ratio and a three line set of printed output is generated. 

Figure 2 4 contains one feature that is not included in the current 
version of the model. The main element of this feature is subroutine SIG, 
which makes a calculation to determine if "significant" savings in accident 
costs are possible. No method for making this calculation is available at 
present. The calculations and test for significant savings in accident 
costs are bypassed when the default values of zero are retained for CFAS 
and CCAS. 



3. Subroutines PREPl and PREP2 

Subroutine PREPl is diagrammed in Figure 25. This routine initial- 
izes variables, sets default values, and if necessary reads data files into 
memory. Only a few of the variables that are initialized are illustrated in 
the flow diagram. The remainder are listed in Table 26. 

Subroutine PREP2 is diagrammed in Figure 26. This routine tests 
the input data to determine that all mandatory input values have been sup- 
plied. If mandatory data are omitted by the user, an appropriate error mes- 
sage is printed. Two of the input tests are illustrated in the flow diagram 
and the remainder are listed in Table 27. Subroutine PREP2 also sets initial 
values for a set of subscripted variables listed in the flow diagram. 



C. Subroutine REED 

The purpose of subroutine REED is to read the input data provided 
by the user. Each of the input data items is described in Section VIII of 
this report. The logic used for subroutine REED is not diagrammed. 

162 



D. Subroutine APT 

The flow diagram for subroutine ADT is shown in Figure 27. The 
annual average daily total flows are calculated for a major and secondary 
highway at the analysis site for each future year which may be included in 
the analysis. A test at the beginning of the routine determines if average 
daily totals for each future year have been supplied directly by the program 
user through input in subroutine REED. 



E. Subroutine SIG 

The purpose of subroutine SIG, a possible future addition to the 
model, is to determine whether "significant" accident savings are possible. 
The routine calculates SIGT, a measure of the potential for reducing 
accidents with countermeasures. The diagram of SIG, shown in Figure 28, 
suggests an approach that could be used to incorporate a test for significant 
savings in accident costs into the model. 



F. Subroutine SIG0 

Subroutine SIG0 is intended for use in conjunction with subroutine 
SIG. If the test for potential accident savings is made and found lacking, 
the program does not proceed. Instead the basis for termination is printed 
by subroutine SIG0. The output uses the same general format and headings 
as the output described in Section IX of this report. However, in SIG0, 
the main heading is TERMINATED ON LACK OF SIGNIFICANT SAVINGS. And, only 
EUAAC(l) and EUAAC(2) are printed. 



G. Subroutine ALIFE 

The flow diagram for subroutine ALIFE is shown in Figure 29. The 
routine calculates the applied life, LAF(KM) , of each countermeasure, (KM), 
to be evaluated at the site analyzed. Prior to calculation each LAF(KM) 
is tested individually to determine if the program user has supplied the 
LAF(KM) in input. (If the user supplies LAF(KM), FCW(KM) must also be 
supplied in input.) 



H. Subroutine FCAPW 

The flow diagram for subroutine FCAPW is shown in Figure 30. The 
routine calculates the final capital worth FCW(KM) per capital item of each 
countermeasure, (KM), after LAF(KM) years of service at the site analyzed. 
Prior to calculation each FCW(KM) is individually tested to determine if 
the program user has supplied the FCW(KM) in input. 

163 



I . Subroutine EACC 

Subroutine EACC is diagrammed in Figure 31. This routine calcu- 
lates, for each requested countermeasure, the equivalent uniform annual capi- 
tal cost, EUACC(KM), and the capital outlay, C#L(KM). These are the project 
costs (rather than unit costs) at the analysis site. The right-of-way costs, 
if any, are included. 



J. Subroutine EFEAS 

Subroutine EFEAS is diagrammed in Figure 32. For each counter- 
measure, KM, specified by the user, this routine establishes the period of 
analysis, IA, and calculates the benefit/cost ratios, BCR(KM), for economic 
feasibility. The routine prints these results in the economic feasibility 
output format presented in Section IX of this report. 



K. Subroutine PFRM 

Subroutine PFRM is diagrammed in Figure 33. This routine calcu- 
lates the benefit/cost ratios, 3CR(KM) , for project formulation. The 
routine prints these results in the project formulation output format pre- 
sented in Section IX of this report. 



L. Subroutine B0C 

Subroutine B0C is diagrammed in Figure 34. It is called in the 
economic feasibility stage by subroutine EFEAS and in the project formula- 
tion stage by subroutine PFRM. Subroutine B0C determines the benefit/cost 
ratios and other cost and benefit measures in both stages of the analysis. 



M. Subroutine SEQ 

Subroutine SEQ is called by subroutine PFRM at the beginning of 
the project formulation stage. This routine arranges the countermeasures 
that are economically feasible in order of increasing capital costs, so that 
the project formulation stage may proceed. The logic for subroutine SEQ is 
not diagrammed. The specifications for this subroutine follow: 

Initial conditions when SEQ is called : Benefit/cost ratios, 
3CRCJJ), have been calculated in economic analyses (in subroutine EFEAS) 
for countermeasures identified by subscripts JJ, where the subscripts are 
JJ = KLST(J), J = 2, MLST. 

164 



It is known that NCEPT of the countermeasures provided benefit/ 
cost ratios t> 1.0 and that NCEPT > 1. 

Purpose of routine SEQ : Select the NCEPT countermeasures with 
BCR(JJ) ^ 1.0 and sort them according to the countermeasure property EUACC(JJ), 
where EUACC(JJ) is the equivalent uniform annual capital cost for the counter- 
measure with subscript JJ. 

Establish the list, ILST (J), J - 1, NCEPT, where the ILST (J) 
are the subscripts of the NCEPT qualifying countermeasures in the sequence 
of smallest EUACC( ) to largest EUACC( ) for J = 1 to NCEPT. 

Note : The original sequence, KLST(J), and its limit, J = MLST, 
are saved for possible use in additional analyses (variations of same case) 
requested in input. 



N. Subroutine COSTS (JJ) 

Subroutine C0STS(JJ) is diagrammed in Figure 35. This routine 
assembles the costs, exclusive of capital costs, for the analysis site with 
countermeasure JJ in the years 1 through IA. This routine employs sub- 
routines SETCST, CALCST, YRM0, YRAC , and YRUC. 



0. Subroutine SETCST 

Subroutine SETCST is diagrammed in Figure 36. The routine is 
called in subroutine C0STS (JJ) prior to the loop which calculates year-by- 
year costs. It sets up initial values and coefficients for the loop and 
also calculates applicable accident and user costs for the zeroth year. 
Subroutine SETCST calls subroutines SKIDI, Cf&RRT, GREDU, DT0UR and DTAjftJ. 
When the routine is exited, the accident rate in the zeroth year has been 
adjusted for the effect of geometric and surface modification countermeasures 
In addition, coefficients have been defined to describe subsequent changes 
in skid number due to traffic wear and subsequent changes in accident rate 
due to changes in ADT and skid number. Finally, the routine defines co- 
efficients for maintenance and operating costs, for future user costs due 
to countermeasure construction and calculates AC0ST, the average cost per 
accident for the severity distribution after countermeasure implementation. 



P. Subroutine SKIDI 

Subroutine SKIDI is diagrammed in Figure 37. The purpose of 
this routine, which is called by subroutine SETCST, is to determine coeffi- 
cients for the calculation of skid number in future years. The routine 
determines values for variables SNY0, SN0, CS, SDF, KW, KSYR and an initial 
value for variable CT. 

165 



Q. Subroutine C0RRT 

Subroutine C0RRT is diagrammed in Figure 35. The primary pur- 
pose of the routine is to calculate GC0R, a correction factor applied to 
the percent accident reduction for geometric and traffic control counter- 
measures. However, the routine also calculates SLGTH, a psuedo- length of 
analysis site for spot locations, and sets values for BO, Bl and Al used in 
the subsequent calculation of the effect of changes in skid number on ac- 
cident rate. 



R. Subroutine GREDU 

Subroutine GREDU is diagrammed in Figure 39. This routine cal- 
culates ALFI and ALPD#, the number of accidents remaining after implementa- 
tion of geometric and traffic control countermeasures for fatal-and-injury 
and property-damage-only accidents, respectively. 



S. Subroutine DT0UR 

Subroutine DT0UR is diagrammed in Figure 40. The routine cal- 
culates AT#UR, the fractional increase in yearly accidents due to counter- 
measure construction, and YUC, the added user costs due to construction de- 
lays and excess fuel consumption. This routine determines all user costs 
currently incorporated in the model. 



T. Subroutine SNADJ 

Subroutine SNADJ is diagrammed in Figure 41. This routine is 
used in a year-by-year loop to correct the accident rate for the previous 
year to the appropriate accident rate for the current year accounting only 
for changes in skid number. 



U. Subroutine CALCST 

Subroutine CALCST is diagrammed in Figure 42. For each year of 
the anaLysis period after the zeroth year, this subroutine updates the skid 
number and adjusts the accident rate for changes in ADT and skid number by 
calling subroutines SKIDC, DTADJ and SNADJ. In addition, the routine calls 
subroutine DT^UR, if necessary, to calculate user costs for countermeasure 
construction in any year after the zeroth year. 



166 



V. Subroutine SKIDC 

Subroutine SKIDC is diagrammed in Figure 43. This routine 
accumulates CT, the total traffic exposure since installation of a counter- 
measure. The routine also (1) updates the skid number for each year, (2) 
decrements KSYR, the remaining life of the surface course, and (3) sets 
KUC = 1, where appropriate, to indicate that construction will occur in the 
year being processed and that subroutine DT#UR must be called. 



W. Subroutine DTADJ 

Subroutine DTADJ is diagrammed in Figure 44. This routine cal- 
culates DTJST, a factor that is used to adjust the previous year accident 
rate to the current rate accounting only for the effect of ADT. 



X. Subroutine ACC0ST 

Subroutine ACCOST is diagrammed in Figure 45. This routine cal- 
culates CTFI and CTPD0, the average cost of fatal-and-injury and property- 
damage-only accidents, respectively, for the area type and highway type in 
which the analysis site is located. 



Y. Subroutine YRM0 

Subroutine YRM0 is diagrammed in Figure 46. This routine cal- 
culates YM0, the maintenance and operating costs for the year being processed, 



Z. Subroutine YRAC 

Subroutine YRAC is diagrammed in Figure 47. This routine cal- 
culates YRAC, the accident costs for the year being processed. 



AA. Subroutine YRUC 

Subroutine YRUC is used to calculate user costs other than those 
due to construction delays and excess fuel consumption. Because such 
additional user costs are not included in the current version of the model, 
YRUC is currently a dummy subroutine. It provides an appropriate place in 
the model for consideration of other user costs that might be added at a 
later date. 



167 



3B. Subroutine DC0STS 

Subroutine DC0STS is diagrammed in Figure 48. This routine cal- 
culates the equivalent uniform annual user costs associated with counter- 
measure construction. If the duration of construction activity (TDUR) is 
zero, the user costs associated with construction are set to zero. Sub- 
routine DT0UR is called in Subroutine DC0STS to calculate the actual user 
costs due to construction and excess fuel consumption. The program then re- 
turns to Subroutine DC^STS where the user costs calculated in Subroutine 
DTOUR are converted to an equivalent uniform annual basis. 



168 



C DURING BENEFIT-COST PROGRAM EXECUTION ALL SYSTEM FILES ARE AVAILABLE IN SLQUENIIAL FORM 



( START J 




irsl cord contain! KSTAT and KSTAR. which ore the STATE CODE, 
,.d Ihe STATE REGION CODE. 



- Blank cord ten 



CALL PREPl ■ 


'' 


CALL REED ■ 


\ 


CALL PREP2 



Set some subscripted variables * 0. 
Read required files into memory. 
Set voriobles to standard initial valu 



Read n 




inder of 


np 


ut data 


for 


one ca 




ncluding 


al 


ernativ 


es for 


weight 


fa 


:tors and 


pe 


iods of 


analysis. 




Determine if significant accident 
savings are possible. 



CALL SIG<2 ' 



^. •— Print basis for non-significant savings. 



GO TO © 



CALL ALIFE 
CALL FCAPW 
CALL EACC 



Calculate applied lives, final capital 
worths, and equivalent uniform 
annual capital costs. 



CALL DC0STS 



Calculate and print result 3 of 
economic feasibility analyses. 



NCEPTj>- *-GO TO@ 




Calculate and print results of 
project formulation analyses. 



NIVAR = NVAR + ] * 



Advance subscripl for next period 
of analysis end weight factors. 



GO TO © 



Figure 24 - Benefit-Cost Flow Diagram 

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170 



TABLE 26 



ADDITIONAL INITIAL VALUES TO BE SET IN SUBROUTINE PREPl 



Set MLST = 1 



Set the following equal to zero: 



Non-Subscripted Variables 



Subscripted Variables 



ANIT 

A0TH 

APD0 

APR 

APREC 

ARA 

ARE 

ASS 

AWET 

IRS 

KWS 

SNY0 

TIM 

TIS 

TLGH 

TMGC 

TSGC 

TSGL 

APED 

SNY0 

BPNY0 

AMDY0 



KCSCD(KM) KM 
KZ<6W(KM) KM = 
PRALL(KM) KM 
PRDAY(KM) KM 
PRDRY(KM) KM 
PRFI(KM) KM = 
PRF0(KM) KM = 
PRH0(KM) KM « 
PRLT(KM) KM « 
PRNIT(KM) KM 
PR0TH(KM) KM 
PRPD^(KM) KM 
PRPED(KM) KM 
PRPR(KM) KM = 
PRRA(KM) KM = 
PRRE(KM) KM = 
PRSS(KM) KM - 
PRWET(KM) KM 
SCMAtf(KM) KM 
SMA0M(KM) KM 
SSMAd(KM) KM 
TDUR(KM) KM » 
UN(KM) KM = 1 
ZLGH(KM) KM = 



= 1, KMAX 

1, KMAX 

= 1, KMAX 

= 1, KMAX 

= 1, KMAX 

1, KMAX 

1, KMAX 

1, KMAX 

1, KMAX 

■ 1, KMAX 

= 1, KMAX 

= 1, KMAX 

= 1, KMAX 

1, KMAX 

1, KMAX 

1, KMAX 

1, KMAX 

= 1, KMAX 

= 1, KMAX 

- 1, KMAX 

- 1, KMAX 
1, KMAX 

, KMAX 
1, KMAX 



171 




Subroutine PREP2 



PRINT - Site description (20A4) 
and message - T0TAL ZER0 YEAR 
ACCIDENTS N0T SUPPLIED 



KC0N = 




KC0N = 1 



PRINT - Site 
Description 



PRINT message - ZER0 

YEAR TRAFFIC N0T SUPPLIED 



Continue tests of input data and 
error messages. See the tcble 
that follows. 




CAPC(l) =CAPC(KWS) 
CCMA0 ( 1 ) = CCMA0 ( KWS ) 
CDFR(l) = CDFR(KWS) 
CMA0(1) =CMA0(KWS) 
CMA0M ( 1 ) = CMA0M ( KWS ) 
CSR(l) = CSR(KWS) 
CR(I) = CR(KWS) 
FCW ( 1 ) = FCW ( KWS ) 
KCSCD(I) = KCSCD(KWS) 
KZ0W(1) = KZ0W(KWS) 
LAF ( 1 ) = LAF ( KWS ) 
LIFC(l) = LIFC(KWS) 
SALV(1) = SALV(KWS) 
SCAPC(l) =SCAPC(KWS) 
SCMA0 ( 1 ) = SCMA0 ( KWS ) 
SDFR(l) = SDFR(KWS) 
SD0R(1) =SD0R(KWS) 
SMA0M ( 1 ) = SMA0M ( KWS ) 
SSMA0 ( 1 ) = SSMA0 ( KWS ) 
TDUR(l) =TDUR(KWS) 
TRL(I) =TRL(KWS) 
UN(! ) = UN (KWS) 
ZLGH(1) = ZLGH(KV/S) 



Figure 26 - Subroutine PREP2 Flow Diagram 



f Return j 



172 



TABLE 27 



TESTS AND MESSAGES FOR SUBROUTINE PREP2 



TestI' 



AALL = 

TIM = 
FWET = 
IATYP = 



or IHTYP = or ISITE = 



KWS = 

LIFF = 

LIFRS = or LIFRB 

TLGH ■ 
MLST = 



Message if Passed 

OVERALL ACCIDENTS FOR ZERO YEAR NOT 

SUPPLIED 
ADT FOR ZERO YEAR NOT SUPPLIED 
FRACTION TIME WET NOT SUPPLIED 
AREA, HIGHWAY, OR SITE TYPE NOT 

SUPPLIED 
AS IS OR AS PLANNED SURFACE SUB- 
SCRIPT NOT SUPPLIED 
REMAINING LIFE OF FACILITY NOT 

SUPPLIED 
YEARS UNTIL RESURFACE OR YEARS UNTIL 

REBUILD NOT SUPPLIED 
LENGTH OF SITE NOT SUPPLIED 
COUNTERMEASURES FOR ANALYSIS NOT 
SUPPLIED 



1/ When any listed test, is passed KC0N should be tested. And^ if KC0N = 
it should be set KC0N = 1 and the site description (20A4) printed 
prior to the message in the table. 



173 



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177 



C Start J 



Resurface 
in zero year. 




C0FC = 1.0 
C<2FF = 1.0 




> LIFRS 



< LIFRS 



C0FC=O. 
C0FF =0. 



Discount future surface 
cost to zero year. 



C0FC = 1./V1 ** LIFRS 
C0FF = 1. 



No future resurface cost 
in period for analysis 



DO 100 J = 1,MLST 

KM = KLST(J) 
K = KM 

DUME = 0. 
DUMS = 0. 



L= LAF(K) 

CRF = (V* VI ** L)/(V1 ** L-l.) 




*0 



DUM = SCAPC(K) 



DUM = CAPC(K) 



DUME = DUME + UN ( K) »CRF» (DUM* C0FC - C0FF»FCW(K)/V1 »»L) 
DUMS = DUMS + DUM • UN ( K) » CG5FC 
CG5FC = 1.0 
COFF = 1.0 




>KM2 




<KM3 



K = KM + K2 



<KM2 



Note: 

Here, both EUACC(KM) 
and C0L(KM) have been 
extended to project cost 
by using the number of 
units UN ( ) required as 
a factor. 



>KM3 



With KM retained as 
countermeasure, prepare 
to process potential 
right-of— way cost and 
life data. 



EUACC(KM) = DUME 
C0L(KM) = DUMS 
100 Continue 



^- Equivalent uniform annual capital 
cost & capital outlay 



f Return J 



Figure 31 - Subroutine EACC Flow Diagram 



178 



f Start J 



Print Headings, Econ. Feasibility 



NCEPT = 
KB= 1 



DO 100 J = 2,MLST 
KC = KLST (J) 



IA = MIN0 (MXYR. LAF(KC)) 



CALL B0C 




#0 



Print: Unable to calculate cost I0K 
for counter-measure JL in year JY. 



I0K =0 



>1.0 



Set Acceptance = Yes 
NCEPT = NCEPT + 1 



<1.0 



Set Acceptance = No 



BCR(KC)=0 



Go to 100 



Print 3 Line Set, Econ. Feasibility 



Go to 100 



EUACC (KC) = EUACC (KC) * (1.0 - C0L (1)/C0L (KC)) 
COL ( KC) = C0L ( KC) - C0L (1) 




LIFRS_ 



Go to 100 



> LIFRS 



L = M1N0 ( LAF ( KC), LAF (1) ) 

DUM = ((V1 ** L- l.)/(V*Vl **L))* EUACC (1) 

EUACC (KC) = EUACC (KC) * (1.0 - DUM/C0L (KC)) 

^ 



Credit surface countermeasure 
with capital outlay already 
committed by prior decision. 




Credit surface countermeasure with present 
capital worth of future costs eliminated by 
countermeasure . 



Figure 32 - Subroutine EFEAS Flow Diagram 

179 



( Start J 



CALL SEQ 



Routine selects the countermeasures which have been found 
economically feasible, CBR (KM) > 1 .0; arranges them in 
order of increasing equivalent uniform annual capital cost; 
and provides the ordered subscripts as ILST ( J ), J = 1 to NCEPT. 



Print Headings, Project Formulation 



KB = ILST(1) 



DO 100 J =2, NCEPT 
KC - ILST (J) 




= 2 



(Long Period) 



IA = MAX<2J(LAF(KB), LAF(KC)) 



= 1 

(Short Period) 



IA = MINv3(LAF(KB), LAF(KC)) 



1A = MIN0(IA,MXYR) 



CALL B0C 






Print: Unable to calculate cost I0K 
for countermeasure JL in year JY. 






J *°. 




I0K =0 













>1.0 



Set Acceptance = Yes 
KB = KC 



Set Acceptance = No 



Challenging 
., — -\ Countermeasure 
Becomes Base 



Go to 100 



Print 3 Line Set, Project Formulation 



100 Continue 



( Return J 



Figure 33 - Subroutine PFRM Flow Diagram 
180 



C stort ) 



CRF = (V* VI +* IA)/(V1 ** IA- 1.0) - 



.- Capital recovery factor for period of analysis, IA years. 



KK (1) = KB 
KK (2) = KC 



JC0N = 3 

I0K =0 

DO 100 JK = 1,2 

JL = KK(JK) 




GO TO 101 



EUAM0(JK) = CDM0 * CRF 
EUAUC(JK) = CDUC * CRF 
EUAAC(JK)=CDAC * CRF 
AM0(JK) = CUMM0/(FL0AT(IA)) 



Equivalent uniform annual costs for bose (subscript 1) and 
alternatives (subscript 2). Also average maintenance and 
_^ — ' operating expenses undiscounted. Items with subscript 1 
appear in first line of 3 line print sets. Subscript 2 items 
ore in second line. 




Alternate countermeasure 
does not involve resurfacing 



N Countermeasure does 
nvolve resurfacing 



= 1 





IRS 



Prior decision for 
immediate resurfacing 



Alternate involving 
resurfacing has applied 
life that extends past time 
for normal resurfacing 



= 



No prior decision for 
immediate resurfacing 



Yes 



UCC (JK) = EUACC (JL) 
C0LD (JK)=C0L(JL) 
EUAUC (JK) = EUAUC (JK) 
+ UCDC1 




LAF(KC)>LIFRS 



No 



> LIFRS 



< LIFRS 



EUAUC (JK) = EUAUC (JK) -UCDC1 



UCC (JK) = EUACC (JL) 
C0LD(JK) = C0L(JL) 



Go to 100 



UCC(JK)=0. 
C0LD(JK) = O. 



100 Continue 



5 



Figure 34 - Subroutine BOC Flow Diagram 



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( Start J 



CUMM0=O. 
CDMO = 0. 
CDUC =0. 
CDAC =0. 



Clear cumulative cost symbols. 



YM<2> = 0. 
YUC = 0. 



Guard against unacceptable 
bits left by loader. 



CALL 5ETCST 



DO 100, JY = 1, IA 
YUC = 0. 



^ Cycle through the years in 
period of analysis. 



CALL CALCST 




o to (T) 



Calculates YM0, the maintenance 
-- and operating costs for year (JY) 

for facility with countermeasure (JJ). 



Go to 



Q 



Calculates YUC, the user costs for 
above year and facility condition. 



Goto (7) 



Calculates YAC, the accident costs 
for above year and facility condition. 



Go 



to© 



CUMM0 = CUMM0 + YM0 



Cumulated maintenance and 
operating costs. 



DF = l./Vl*»JY 



Discount factor for year JY. 



CDM0 = CDM0 + YM0 * DF 
CDUC =CDUC +YUC * DF 
CDAC =CDAC +YAC » DF 



Present worths of maint. & operating 
costs, user costs and accident costs 
for years one through JY. 



100 Continue 



G> 



f Return J 



Note: Argument, (JJ) in call is the 
subscript for countermeasure. 



Figure 35 - Subroutine C0STS(JJ) Flow Diagram 



183 



Subroutine SETCST 



f Start J 



Call SKIDI 



Call C0RRT 



Call GREDU 



AC0ST = (ALFI * CTFI + ALPD0 * CTPD0)/(ALFI +ALPD0) 

JY = 

DTJST = 1.0 

ARC = (ALFI + ALPD0) * 1.0E06/((TIM +TIS) * 365. * SLGTH) 




Calculate average cost of 
accidents after reduction 
due to geometric and control 
countermeasures. Calculate 
overall accident rate 
(accidents/ 10° veh. miles) 
prior to any reduction in 
zero th vear due ro skid 

number changes. 





Call DT0UR 






I 


1 






CDAC = AT0UR * AC0ST * SLGTH * 365. 


* (TIM +TIS) * ARC/1.0E06 



AT0UR = 0. 
AJDT = 1. 



Call DTADJ 



Call DTADJ to obtain an 
initial value of AJDT 



CDAC, the accumulated 
discounted accident costs 
are incremented in the 
zero year if countermeasure 
construction zone is required 
with resultant increase in 
zero year accidents. User 
costs are incremented in 
DT0UR. The base case "as 
is" or as planned values 
calculated separately in 
DC0STS. 



DTJST = 1 . 



Call SNADJ 




Adjust zero year accident rate for 
changes, if any, in zero year skid 
number. 



<SCMA0(JL)> 



*0 




= 



CM0 = UN(JL) * SCMA0(JL) 
CCM0 = UN(JL) * SSMA0(JL) 
CM0M = UN (JL)* SMA0M(JL) 



CM0 = UN(JL) * CMA0(JL) 
CCM0 = UN(JL) *CCMA0(JL) 
CM0M = UN(JL)* CMA0M(JL) 



BM0 = TLGH(JL) * ACMA0(IATYP.IHTYP) 



( Return J 



Figure 36 - Subroutine SETCST Flow Diagram 



184 



Subroutine SKID1 
(Initiate Skid Number Calculations) 

SNTEX (XBPN,XMD) = (1.38* XBPN - 31.)/EXP (1.64/XMD " .47) 



CED 





SNY0 



SNY0 = SNTEX (BPNY0.AMDY0) 



KW=JL 

ABPN = BPNR (KW) 

AMD = AMDR ( KW) 



<D* 



Countermeasure does 
not involve resurface 
or surface treatment. 
Use "as is" or as 
planned surface . 



KW = 1 

ABPN = BPNR (I) 

AMD = AMDR (!) 



"C 




Countermeasure involves 
/ resurface or surface 
treatment. 










Initial base 
condition. Use 
"as is" or as 
planned surface . 














> = 1 


CT = 0. 

KSYR = AMIN<2(LIFC(KW).UFRB) 


> \ 







No prior decision for 
immediate resurfacing 



Prior decision to 
resurface immediately 



KSYR -AMIN<Z)(LIFRS,LlfRB? 



Current (year = 0) 
skid number is not 
supplied. Use sfd. 
average until 
surface is renewed. — 



SD0 = SD0R (KW) 




SD0 = SNTEX (ABPN, AMD) 



SD0 = (SD0 + SDFR (KW)]/2 
SNY0 = SD0 




SNY0 = SBAR(IATYP) 



SD0 = SNTEX (ABPN. AMD) 
SN = SD0 



-^To© 



Set CT * 0. so that 
CT = 0. can be used 
as clue that new sur- \^- 
face or treatment is 
applied in zero year. 



CS =0. 
CT = 10. 
SDF = SD0 
SN = SNY0 



SD0 = SNY0 

1 

I 
L 



AD0 = SNTEX (ABPN. AMD) 



AD0 = SD0R (KW) 



Skid number does not 
vary or current value 
is outside normol 
bound. 



SN =SNY0 

CT = (EXP((SNY<Z) - SD0)/CSR( KW)))* 100000. 



©— 



CS =CSR(KW) 
SDF = SDFR(KW) 



3 



SN0LD = SNY0 



( Return J 

Figure 37 - Subroutine SKIDI Flow Diagram 



185 



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186 



Subroutine GREDU 



f Stort ) 



AFI = AALL* PFI (ISITE, IATYP. IHTYPJ/100. 
APD0 = AALL* PPD0 (ISITE, IATYP. IHTYP)/100. 



ALFI = AFI 
ALPD0 = APD0 




TE5T 


ISITE = 


JSITE(JL) 




IATYP 


= JATYP(JL) ? 




IHTYP 


= JHTYP(JL) 


IF NO 


- WARN USER 





ALFI = AALL- (PRALL( JLj/100.) * AALL • (PFI(ISITE. IATYP, IHTYP)/100.) • GC0R 
AU>D0 = AALL- (PRALL(JL)/I00.) • AALL * (PPD0(ISITE, IATYP. IHTYPJ/100.) * GC0R 



AFI =AALL • (PFIflSITE. IATYP, IHTYPJ/100.) 
APD0 = AALL • (PPD0(ISITE. IATYP. IHTYPJ/100.) 



ALFI = AFI - (PRFI(JL)/100.) • AFI * GC0R 

ALPD0 = APD0 - (PRPD0(JL)/1OO.) » APD0 * GC0R 



AH0=AALL • PH0(ISITE. IATYP. IHTYPJ/100. 
ARE =AALL • PRE(ISITE. IATYP, IHTYPJ/100. 
ASS=AALL * PSS(ISITE. IATYP. IHTYPJ/100. 
ARA=AALL • PRA(ISITE, IATYP, IHTYPJ/100. 
ALT = AALL • PLT(ISITE, IATYP, IHTYPJ/100. 
APR = AALL • PPRflSITE, IATYP, IHTYPJ/100. 
AF0=AALL • PFOflSITE. IATYP. IHTYPJ/100. 
APED = AALL • PPED(ISITE, IATYP. IHTYPJ/100. 
A0TH =AALL • P0TH(ISITE. IATYP. IHTYPJ/100. 



ARH0 =(PRH0(JL)/1OO.) • AH0 • GC0R 
ARRE = (PRRE(JL)/100.) • ARE • GC0R 
ARSS = (PRSS(JL)/100.) • ASS • GC0R 
ARRA = (PRRA(JL)/100.) • ARA • GC0R 
ARLT = (PRLT(JL)/I00.) • ALT • GC0R 
ARPR = (PRPR(JL)/I00.) * APR • GC0R 
ARF<2 = (PRF0(JL)/1OO.) • AF0 • GC0R 
ARPED = (PRPED(A)/100 ) • APED • GC0R 
AR0TH = (PR0TH(JL)/1OO.) • A0TH • GC0R 
ART0T = ARH0 + ARRE + ARSS + ARRA + ARLT + 

ARPR +ARF0 + ARPED + AR0TH 
ALFI = (AALL - ART0T) • PFI(ISITE. IATYP. IHTYPJ/100. 
ALPD0 = (AALL - ART0T) • PPD0(ISITE. IATYP. IHTYPJ/100. 




AWET=AALL • PWETflSITE, IATYP. IHTYPJ/100. 
ADRY=AALL • PDRY(ISITE. IATYP, IHTYPJ/100. 



ARWET =(PRWET(JLJ/100.) * AWET • GC0R 

ARDRY = (PRDRY(JL)/100.) • ADRY * GC0R 

ART0TAL = ARWET + ARDRY 

ALFI = (AALL - ART0T) • PFIflSITE. IATYP, IHTYPJ/100. 

ALPD0 = (AALL - ART0T> • PPD0(ISITE. IATYP. IHTYPJ/100. 



ANIT=AALL • PNIT(ISITE. IATYP, IHTYPJ/100. 
ADAY=AALL • PDAY(1SITE. IATYP. IHTYPJ/100, 



ARNIT = (PRNIT(JL)/100.) . ANIT • GC0R 

ARDAY = (PRDAY(JL)/100.) . ADAY • GC0R 

ART0T = ARNIT +ARDAY 

ALFI = (AALL - ART0T) « PFIflSITE. IATYP. IHTYPJ/100. 

ALPD0 = (AALL - ART0T) • PPD0(ISITE. IATYP. IHTYPJ/100. 




AFI = AALL * (PFIflSITE, IATYP, IHTYPJ/100.) 
APD0 = AALL • (PPD0(ISITE, IATYP. IHTYPJ/100.) 



ALFI = AFI - (DPRFI(JL)/100.) • AFI * GC0R 

ALPD0 = APD0 - (DPRPD0(JL)/1OO.) • APD0 * GC0R 



>0 



Figure 39 - Subroutine GREDU Flow Diagram 



187 



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CD 
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c 
o 
o 



ON 

CO 

CO 

n 

3 
60 
•H 
pM 



Subroutine DT0UR 



Q 




•© 



AT0UR = TDUR(JL) * ADR/365. -- 



Froctionol increose in 
. _ accident rate for year 
in which counlermeosur 
construction work is do 



SADT = (TIM t TIS)/ 1000. SADT ' (ADTM(JY) + ADTS(JY))/ 1000 




ZL = ZLGH(JL) 




ZL = ZL + .05 



CD - CDI(KZ. KA. KSCD) + CDL(KZ, KA. KSCD) * ZL 

CD1 = CDI1 (KZ, KA. KSCD) + CDL1(KZ, KA, KSCD)* ZL 

CD2 = CDI2(KZ, KA. KSCD) +CDL2(KZ. KA. KSCD)* ZL 

CD3 = CDI3(KZ, KA, KSCD) + CDL3(KZ, KA. KSCD)* ZL 

DD =DDI(KZ, KA, KSCD) 

DD1 = DON (KZ, KA. KSCD) 

DUM = ((( (SADT *CD3 + CD2)* SADT +CD1)* SADT +CD)/(DD + DD1*SADT))*ZL 

Comment: Here. DUM is the vehicle hours of delay incurred during one day of 

schedule KSCD at one work site of length ZLGH(JL). 



CD = FDI(KZ, KA, KSCD) +FDL(KZ, KA, KSCD) • ZL 
CDI = FDI1 (KZ. KA. KSCD) + FDL1 (KZ. KA, KSCD) « ZL 
CD2 = FDI2(KZ. KA, KSCD) +FDL2(KZ, KA, KSCD)* ZL 
CD3 = FDI3(KZ, KA, KSCD) +FDL3(KZ, KA, KSCD)* ZL 




CD =CD + DUM * CIDLE 



CD =CD + FDF(KZ. KA, KSCD)* CIDLE 
CD) =CD1 + FDF1 (KZ, KA. KSCD) * CIDLE 
CD2 =CD2 +FDF2(KZ, KA, KSCD)* CIDLE 
CD3 =CD3 +FDF3(KZ, KA, KSCD) -CIDLE 



YUC =(TDUR(JL)*TLGH/ZLGH(JL))* ((CVHD * FUTC (NVAR ) * DUM) 
+ CFUEL*(((SADT « CD3 +CD2) • SADT +CD1) * SADT +CD)) 




User delay costs plus excess 
fuel consumption costs due to 
countermeosure construction. 



Zero rn year addition 
incorporated without discount. 



f Return J 



Figure 40 - Subroutine DT0UR Flow Diagram 



189 



Start 



I 



") 



Routine increments accident rate to adjust 
for change in skid number from previous year. 



ARC = ARC * DTJST 



R2LUA 
RMLUA 
RMLCA 
U2LUA 




Adjust accident rate for changes in ADT. 



?-© 



DUM = accident rate (accidents/10 o veh. miles) 

above which there is sensitivity to skid number. 
7 



^ 



DUM = 1.3339 * FWET + 1.082 



X 



UMLUA 
UMLCA 



DUM= .6206 * FWET + 1.082 



/ 



DUM = accident rate (accidents/ 10" veh. miles) 
above which there is sensitivity to skid number. 




DRDS =(ARC - DUM) * FWET * (-.04264)/ 

(FWET * (Bl - 1. - .04264 * (SN0LD - SBAR (IATYP))) + 1.) 
DRDS = AMAX1 (DRDS, - .0825 * FWET) 
ARC = ARC + DRDS * (SN - SN0LD) 



I 



f Return \* MM 



Figure 41 - Subroutine SNADJ Flow Diagram 



190 



u 

—I 

< 

u 

0) 

c 

3 

2 

_Q 

3 




/O* 




s 

to 
u 

60 
CO 



H 
en 

u 
< 

4) 

c 

■H 
4J 

3 
O 

u 

3 

en 



0) 
M 
3 
O0 



191 



Subroutine SKIDC 
(Skid Number Calculation) 



( Start J 
1 



SN0LD=SN _- — 



Save Previous Year 
Skid Number 




KUC - 1 

KSYR = LIFC(KW) 

CT =0. 




SD0 =SD0R(KW) 



SD0 = (1.38 * BPNR (KW)- 31 .)/EXP(l .64/AMDR (KW) ** .47) 



KUC =0 



CS =CSR(KW) 
SDF = SDFR(KW) 



M9" 



DUM = (ADTM(JY) +ADTS(JY) * S65./2. 

CT = CT + DUM 

SN = SD0 +CS * AL0G(AMAX 1(1.0, CT/100000.)) 



<0. 




SN = AMAXKSN, SDF) 



SN = AMIN1 (SN, SDF) 



CT =CT + DUM 
KSYR = KSYR- 1 



f Return ) 



Figure 43 - Subroutine SKIDC Flow Diagram 



192 



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194 




DUM = FL0AT (LIFC(JL)- KSYR - 1) 

YM0 = CM0 + DUM * CCM0 

YM0 = AMIN1 (YM0, CM0M) + BM0 



-: 



f Return J 



Figure 46 - Subroutine YRM0 Flow Diagram 



195 



4 



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196 



Subroutine DC0STS 



Start 



TDUR (1) 



ko 



= o 



<Q IRS V^K 


LAF(1)^> 
^LIFRS 


>LIFRS 


JY = LIFRS 




T= i 






1 


JY = 




UCDC1 =0. 


—To© ^ 


1 


— c 

1 


D 






Call DT0UR 







l 



DUM = (AT0UR * AALL * (CTPD0 * PPD0(ISITE, IATYP, IHTYP) 

+ CTFI * PFI (ISITE, IATYP, IHTYP)) +YUC)/V1 ** JY 
L = LAF<1) 
UCDC1 = DUM * (V * VI * * L)/(V1 * * L - 1 . ) 



— <D 



f Return J 



Figure 48 - Subroutine DC0STS Flow Diagram 



197 



APPENDIX F 



SUBROUTINE HIERARCHY 



Routine Name 

ACC0ST 

ADT 

ALIFE 

BCMAIN 

(main program) 



B0C 

CALCST 

C0RRT 



DC0STS 
DTADJ 

DT0UR 



EACG 

EFEAS 

EXIT 

FCAPW 

GREDU 



Calls 


Is Called Bv 


__ 


BCMAIN 


— 


BCMAIN 


— 


BCMAIN 


ACC0ST 


__ 


ADT 




ALIFE 




EACC 




EFEAS 




EXIT 




FCAPW 




PFRM 




PREPl 




REED 




SIG (dummy routine) 




SIG0 (dummy routine) 




SIGT (dummy routine) 




C0STS 


EFEAS 


DTADJ 


C0STS 


DT0UR 




SKI DC 




SNADJ 




— 


SETCST 


CALCST 


B0C 


SETCST 




YRAC 




YRM0 




YRUC 





DTtfUR 



B0C 



BCMAIN 
CALCST 
SETCST 
CALCST 
DC0STS 
SETCST 

BCMAIN 
BCMAIN 
BCMAIN 

BCMAIN 

SETCST 



198 



Routine Name 

PFRM 

PREPl 
PREP2 

REED 

SEQ 
SETCST 



SKIDC 
SKEDI 
SNADJ 



Calls 

E0C 
SEQ 



C0RRT 
DTADJ 
DT0UR 
GREDU 
DTADJ 
DT$UR 



Is Called Bv 

BCMAIN 

BCMAIN 
BCMAIN 

BCMAIN 

PFRM 
C0STS 



CALCST 
SETCST 
CALCST 
SETCST 



YRAC 
YRMO 
YRUC (dummy routine) 



C0STS 
C0STS 
C0STS 



199 



APPENDIX G 
SYMBOL NAMES AND DEFINITIONS 



This appendix provides a description of symbol names used in the 
computer flow diagrams. A code, presented in Table 28, has been employed 
to describe some aspects of the symbols. 



TABLE 28 

CODE DEFINITIONS FOR SYMBOLS 

Code No. Definition 

1 Input, mandatory. 

2. XX Input, conditionally mandatory, 

(Conditions are described in 
note number XX) . 

3 Input, optional. 

4 Input from system files. 

5 Internal to program. 

6 Output 

7 For potential logic that could 

be added in the future. 



Table 29 presents the symbol names, the code numbers, the esti- 
mated dimensions, and the definitions. 



200 



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—IMC 



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cr d 





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3 3 3 3 tH 

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203 



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213 



NOTES FOR TABLE 29 
No. of Note Note 

01 ADTM(JY) and ADTS(JY) JY = 1, 20 constitute one of three 
ways to input ADT projections. One of options must be used. 
ADTS ( ) required only at an intersection site. Other options 
are compound growth and linear growth; see TMGC, TMGL, TSGC 
and TSGL. 

02 FCW(KM) is mandatory input for a countermeasure (KM) for 
which the user has supplied LAF(KM) as input. FCW(KM + K2) 
is mandatory input for countermeasure KM that requires non- 
zero right-of-way costs. Otherwise, FCW(KM) is normally 
calculated in program. 

03 Input is mandatory for a countermeasure, JL, that requires 
a work site for construction. 

04 KWS should be provided as input if the M as is" or "as planned" 
surface is not the standard type with subscript 1. Other- 
wise program will use skid and cost characteristics of sub- 
script one. 

05 LAF(KM + K2) is mandatory input for the life or amortiza- 
tion period of the right-of-way with non-zero costs for 
countermeasure KM. Otherwise, LAF(KM) is optional input 

if the program user wishes to override the value calculated 
internally by the computer program. Note that FCW(KW) is 
also mandatory if LAF(KM) is supplied in input. 

06 Input is mandatory for at least of these when program user 
specifies a geometric or traffic control countermeasure that 
is not part of the system file. In this case, KM will be a 
subscript that is unused in files. 

07 SCAPC(KM) is optional for any countermeasure where CAPC(KM) 
is available from system files and user overrides with 
SCAPC(KM). SCAPC(KM) is mandatory input for unfiled counter- 
measure KM with characteristics supplied by user. SCAPC(KM + K2) 
is mandatory for non-zero capital cost per unit of right-of-way 
for countermeasure KM. 

08 TIS is required as input if site is an intersection. 



214 



NOTES FOR TABLE 29 (Concluded) 
No. of Note Note 

09 TMGC is mandatory input if the projected ADT are based on 
a compound growth. 

10 TMGL is mandatory input if the projected ADT are based on 
a linear growth. 

11 TSGC is mandatory if site is an intersection (ISITE = 3) 
and projected ADT are based on a compound growth. 

12 TSGL is mandatory input if site is an intersection (ISITE = 3) 
and projected ADT are based on a linear growth. 

13 UN(KM) are mandatory input for all countermeasures (KM) to 
be evaluated at the site under analysis. In addition, in- 
put for UN (KM + K2) may be required for right-of-way units 
associated with KM. And finally, UN(1) or UN(KSW) may be 
required to quantify the costs of pavement alterations set 
by prior decision for the zeroth year or for anticipated 
future schedules. 

14 ZLGH(JL) are mandatory for those countermeasures (JL) that 
have been specified for evaluation in input and also require 
construction TDUR(JL) > 0. Also, either ZLGH(l) or ZLGH(KSW) 
will be required depending on site conditions in the zeroth 
year. Failure to supply a needed ZLGH( ) will cause the 
associated construction site length to have a minimum value. 

15 AMDY0 must be supplied as input if BPNY0 is supplied. (They 
will be used only if SNY0 is not input.) 



215 



APPENDIX H 



CONTROLLING SKIDDING BY INFLUENCING DRIVER BEHAVIOR 

One way to control skidding is to regulate the behavior of the 
driver so that, in effect, demands for skid resistance of a highway surface 
are decreased. Regulation has several aspects such as getting the driver 
to reduce speed when the surface is wet, getting him to drive less errati- 
cally and thus decrease the possibility of positioning the vehicle so that 
a skid is likely, and teaching him to recognize potential skidding condi- 
tions and/or what to do when a skid once begins. Unfortunately, no studies 
presently exist dealing directly with skidding from the driver's standpoint, 
so the closest that we can come is to consider general factors that control 
(or do not control) driver behavior. The following is a discussion of this 
topic, with emphasis placed on speed control because speed is perhaps the 
single most important factor in the genesis of a skid. Six specific sub- 
ject areas are covered: training, static signing, dynamic signing, signing 
relevancy, delineation, and vehicular factors. Law enforcement techniques 
are not considered. A conclusion section follows the six areas. 

1. Training : The possibility of training drivers to make appro- 
priate control actions when a skid begins has undoubtedly been considered 

since driving began, but surprisingly little seems to have been done to 

07/ 
implement the idea. Forbes—' stressing the importance of such training, 

commented that skidding is a dominant factor in accidents and recommended 

that skid instruction be given in driver education courses. Some progress 

was made in the next few years. Later, an article in the American Journal 

of Insurance (1969) discussed skid schools and various facilities including 

simulators that existed for training drivers to handle panic situations like 

skids. The article concluded that such facilities offered the possibility 

of "crisis conditioning" under safe circumstances. 

The extent to which skid-control training facilities exist today 
cannot be known without a formal survey. Hanscom^L' lists the Liberty 
Mutual Insurance Company's Skid School, a school that trains race car 
drivers to take curves at the highest possible of levels without skidding, 
and the Penn State University Skid Simulator. There are more, of course, 
but only a formal survey can tell how many. 

A literature search failed to yield any studies dealing with the 
effectiveness of skid training. It is assumed that it is, or at least 
could be, effective but data must be obtained to make sure. A straight- 
forward study in which one group of driver education students receives 
skid training while a similar group does not could easily be made, with the 
two groups being compared for the types and severity of accidents that they 
have for several years after the instruction. From these data the cost- 
effectiveness of such training could be calculated. 

216 



Finally, it should be noted that the literature has nothing to 
say about the possibility of training drivers to recognize potential skid- 
ding conditions. It would seem that this possibility should be explored; 
perhaps drivers, especially inexperienced ones, could profit greatly from 
such training. 

2. Static signing: Static signs are signs unenhanced by lights 
or any other attention-getting device. Studies will be considered in three 
categories: identification frequencies, effectiveness, and parameters 
affecting identification. 

a. Identification frequencies: HakkinerK-?/ placed test 
signs ahead of a curve, then stopped drivers and asked them to tell what 
they remembered of the signs after passing them. Only 28% recalled a 
general warning sign but 627 recalled it when supplementary information 
was added. Seventy-eight percent recalled a 70 km speed limit sign while 
807o recalled a 50 km limit sign indicating that fairly large differences 
in allowable speed did not affect perception. Blackburn, Glauz, Kobett, 
and Sharp2/ reported that 65% of drivers passing an ice warning sign on a 
bridge recalled seeing it. In a recent study, Summala and Naathanen22/ 
had subjects drive over a 257 km course with instructions to name all 
traffic signs they saw along the route. They reported about 97% of the 
signs, and the authors concluded that earlier experimental results indicat- 
ing that drivers see relatively few signs probably reflect a lack of moti- 
vation. This seems to be reasonable; undoubtedly, if drivers searched 
diligently for information they would find more than they normally do and 
would probably act on it to a greater extent. The problem, of course, is 
to find some means of providing the rnotiviation. 

b. Effectiveness : Several early studies reported that 
static signing had little influence on speed (0ttini,527 Rowan and Keese,— ' 
Brackett,™ BallingerH/ ) . Later studies both support and dispute these 
findings. Hammer™ found that standard curve warning signs did not reduce 
accidents by themselves but that they did when advisory speed signs were 
added. Accidents considered were the nighttime, single vehicles, running- 
off-road type. The City of Wayne, Michigan, installed overhead lane-use 
control signs on a one-way street ahead of a particular intersection 
(Hoffman—'). Total accidents at that intersection went down 44% in 1 year 
while those due to turning from the wrong lane went down 58%. It was 

1 Q / 

claimed that this saved the city $47,900 for the year. Culp and Dilhof f—' 
placed static signs reading "watch for ice on bridge" at 24 different loca- 
tions and stated that this reduced accidents. However, Stewart and SequeiraHit/ 
reported that static ice or frost warning signs were ineffective; these 
authors believe that this was so because motorists see these signs so fre- 
quently that they cease to pay attention to them. 



:i? 



In still another study, Ritchie^.' found that subjects 
drove faster and produced more lateral acceleration in curves when a curve 
and speed advisory sign were present than when they were not. He also 
reported that drivers exceeded advisories of 15 to 35 mph but not those 
of 45 to 50. Recently, Rutley£±' reported that speeds of vehicles 
in curves approached those of the advised maximum advisory speeds displayed 
on signs; in some cases vehicles reduced speed and in some cases they 
increased it. Rutley also reported that these speed advisory signs, placed 
at 150 curves in three counties in England, reduced accidents by 44% in one 
county but did not affect accidents in the other two. The author pointed 
out that the advised speeds were developed under carefully controlled 
conditions and were those that yielded the maximum speed but still gave 
comfortable radial accelerations to drivers and passengers. 

Evidence for the effectiveness of static signs is thus con- 
flicting. Nevertheless, it should be pointed out that most of the negative 
evidence comes from earlier work, and that perhaps some of the later work, 
avoided some of the mistakes made earlier and thus tended to yield positive 
results. There is a suggestion in those studies yielding positive results 
that the circumstances in which signs are used may be a critical factor in 
determining effectiveness. RitchieA^' reported that speeds increased 
when 15 to 35 mph advisories were encountered but did not change when 45 
to 50 mph advisories were encountered while Rutley_' found that speeds 
increased in some cases and decreased in others. Rutley also found dramatic 
accident reduction in one county but none in two others. Unfortunately, 
these data do not suggest what factors promote effectiveness although the 
work discussed in the immediately following subsection and the two sections 
after that offer some ideas. We conclude here that static signing can be 
effective in regulating speed but is not necessarily so. 

c. Parameters affecting identification : In a laboratory 
study whose purpose was to determine the effectiveness of lane drop signs, 
Burg—' showed movies and still pictures of signs. He found that they 
preferred a 4 x 8 ft rectangular sign over several 40 x 40 in. diamond- 
shaped signs and that the preferred message of several was "lane end" in 
a line above "merge left." As variables, shape is confounded here by 
size so it is impossible to conclude anything about preferences for either 
variable, but we can conclude that type of message is important. In a 
study previously cited, HakkinenM/ also found that road familiarity did 
not affect motorists' noticing an ordinary sign but did when supplementary 
information was added in that they saw the sign more then. Ferguson and 
CookiLl/ used questionnaires to evaluate drivers' awareness of sign color 
and shape. They found that drivers do not pay much attention to color 
except that they recognize red, white, and yellow the most often.. They 
also found that shape and message type were the most important variables 
determining sign effectiveness. 

218 



23/ 
Eklund — performed a laboratory study to determine what 

factors influence drivers' recall of signs. Important variables were found 
to be brightness, brightness contrast, simplicity, difference from other 
signs, and frequency of appearance; as would be expected, increasing amounts 
of all of these variables enhanced recall. Cameron — had subjects 
classify signs by their function into one of four categories. The depend- 
ent variable was classification time. Among other findings he reported 
that signs with symbolic messages were superior to signs with verbal 
messages. Backlund— questioned drivers about various aspects of a 
sign they had just passed. He found that those familiar with the road 
gave the largest number of correct answers, sign violators gave the least 
number of correct answers, and sparse traffic decreased drivers' awareness 
of the sign. To determine how signal visibility affects accidents, Kassan 
and Crowderd2.' improved the visibility of signals at 68 intersections 
in Los Angeles. This treatment at a cost of less than $5 ,000/intersection 
reduced the most commonly occurring types of accidents. 

To summarize these findings, some factors that influence 
driver's sign perceptions are message content and type (with evidence that 
symbolic messages are superior to verbal ones) ; frequency of occurrence of 
the sign and the amount by which it differs from other signs; simplicity 
of the sign and its brightness, brightness contrast, and visibility; and 
familiarity with the road on the part of the driver. It is noteworthy 
that many of these factors are the same as those manipulated by advertisers 
such as message content, intellectual level, frequency, uniqueness, and 
intensity. There are undoubtedly other important factors and it would be 
prudent to identify them. 

3. Dynamic signing : This section reviews studies in which 
the information to be imparted by static signs is enhanced by lights or 
any other attention-getting device. In one of the earliest of these, 
Brackett — investigated the value of adding a yellow flashing beacon 
to existing signing, and found that this had little or no effect in reduc- 
ing vehicle speeds under various conditions. Blackburn et al.— 
reported that vehicle speeds were about 7 mph or 11% lower when a sign 
reading "icy bridge ahead" plus a flashing signal was present 1/4 mile 
upstream of a bridge than when neither sign nor flashing signal was present. 
In a study testing how adding a traffic signal to a rural crossroad affected 
approaching vehicles' speeds, Bleyl— found that the signal caused 
drivers to approach the intersection more cautiously than they did before 
under several conditions. 



219 



In a discussion of problems of driving in fog, Schwab—' 
stated that directional types of fixed-lighting systems have proved to be 
effective in guiding drivers in fog at night. He also stated that variable 
message signs that warn of fog and indicate desirable speeds are the best. 
Hanscom— ' studied drivers' responses to two types of skidding hazard, 
wet pavement and icy bridges. He found that signing these hazards without 
flashing lights was^not effective (in contradiction to the earlier findings 
of Culp and Dilhof f— ) but that adding warning lights reduced speeds. 
Speed reductions in the approach to the bridge averaged about 3 mph during 
the day and 5 mph during the night. The most effective sign pattern was 
one in which a sign appeared ahead of the bridge as well as on it. A 
questionnaire elicited the information that hazard cues were roadway curva- 
ture and superelevation, behavior of other vehicles, appearance of the 
pavement's surface, ambient conditions, known site accident history, and 
the skid warning sign (only four out of 305 respondents or 1% said this 
last was their cue of a potential skid hazard). 

In a study of the effects of five signing configurations warning 
drivers of an upcoming school zone, Rosenbaum, Young, Byington, and Basham — ' 
found that dynamic signing was superior to static signing in getting motor- 
ists to reduce speeds in the school zone and that, in general, increas- 
ing the amount of information decreased speeds to a greater extent. The 
most effective condition was one in which five signs were used including 
one in which lights flashed on a sign saying "speed violation when flashing" 
when the speed limit was exceeded. In this condition the amount of speed 
reduction of automobiles from 2,600 to 200 ft of the school was 20.6 mph 
or about 507o whereas in the static signing condition the reduction in the 
same interval was only 1.6 mph or about 5%. 

In summary, dynamic signing is superior to static signing and 
adding attention-getters to static signs improves their effectiveness. 
Work that has been done to investigate dynamic signing has not been syste- 
matic; usually some kind of attention-getter such as a flashing light is 
added to an existing static sign and the effects on traffic flow studied. 
Systematic work involving such variables as sign location, message type, 
and signal intensity would seem to be in order. Finally, a note of caution 
regarding the use of novel signs, especially dynamic ones, should be made. 
If they are used too frequently, drivers can be expected to ignore them 
because their attention-getting value will diminish; adaptation such as 
this is well-established in behavioral science work. 



220 



4. Signing relevancy : This title refers to the fact that 
stimuli designed to regulate drivers' behavior must be relevant to their 
needs and capabilities in order to be effective. In 1949, Wiley observed 
that traffic ignores posted speed limits and that people drive not by the 
speedometer but by prevailing traffic, roadway, and environmental condi- 
tions. Jackman— studied several ref lectorized and nonref lectorized signs 
reading "slow" and "stop" and found that the "slow" sign was ignored if 
put where it was not warranted. In a study comparing reactions to signs 

of different kinds, Howard— concluded that the perception of signs in- 
creases sharply the more "reasonablv" the sign relates to roadway condi- 

12/ 
tions. Brackett — stated that signing had no effect on speed and that 

people drive according to highway geometries and Bezkorovainy§/ reiterated 

this when he said that speeds in curves were not related to posted advisory 

speeds but to curve geometries. 

Ballinger—' studied the operation of two ice warning systems and 
observed that signing "inconsistent with prevailing conditions" was gen- 
erally disregarded by motorists. In commenting on motorists' attitudes, 
Williams and Van Der Nest—' said that "instead of accepting the warnings, 
commands, or information presented by road signs, the road user prefers 
to draw his own conclusions from his observations of the road, and to act 
on them in preference to the signs." A similar view was espoused by Forbes, 
et al. (quoted in Hanscorn£2/) , who stated that motorists were most likely 
to respond to warning signs in the presence of perceived hazards. Blackburn, 
et al.— ' also found that drivers responded better to ice warning signs when 
the perceived hazard was present, as did Hanscom.^H.' 

Some of these investigators are clearly pessimistic about the 
ability of signs to regulate driver behavior. However, the definite belief 
of several others is that one important factor determining whether or not 
drivers pay attention to signs is their relevancy to that to which they 
refer. If drivers think a sign's information is relevant or meaningful, 
they will heed it; if not they will ignore it. The principle is clear: 
sign information (and undoubtedly any other regulatory stimuli) must 
accurately reflect whatever it is that is referred to, and it must be 
realistic in terms of the capabilities and limitations of the driving popu- 
lation or it will be useless and a waste of money. 

5. Delineation : As used here, delineation techniques include: 
lane lines, edge lines, and other lines or colors painted or laid on pave- 
ment, raised pavement markers, rumble strips, and reflectors installed on 
the pavement or mounted on posts at the side of the road. With regard to 
speed control, several studies have concerned themselves with edge lines. 
Most have yielded negative results despite a report by Williston—' 

that they increased speeds in general and one by the Arizona Department 



221 



of Highways— that they increased speeds at night. Taragin— ' reported no 
effects nor did Powers and Michael.—' A study by the Missouri State High- 
way Commission—' also reported no effects and, more recently, a study by 
David—' found that implementing delineation treatments such as adding a 
freshly painted center line, raised pavement markers, and post markers had 
no effects. 

Evidence exists that more dramatic delineation treatments have an 

2/ 
effect on speed. Anderson and Pederson— ' put 12-in. wide ref lectorized 

colored edge lines, colored post delineators, and colored guide signs on 
entrances and exits of a freeway cloverleaf interchange. Entrances and 
exits were blue or yellow. Behavioral effects were found on the exits only: 
blue exits had higher exit speeds and later points of exit than normal, 
while yellow exits had the reverse effects. Only 257, of the drivers were 
aware of the color treatments. In a study involving colored pavement, 
Gwynn and Selfort£±/ paved a freeway exit ramp red and found they day- 
time speeds were lower after the ramp was colored but that there was no 
effect at night. 

Transverse white lines have been painted across driving lanes at 
exponentially decreasing distances apart to try to get drivers to reduce 
speed faster than normal as they approach situations such as intersections 
or toll booths. They are reported to be effective although no American 
studies attesting to this turned up in the literature search upon which this 
section of the report is based. However, a recent report concerning 
English roads by Rutley^L' supports the idea. In his study, Rutley 
painted these kinds of lines at the ends of lengths of high-speed four- 
lane highways at eight sites. Each site had 90 yellow lines 0.6 m wide 
covering the last 0.4 km before the intersection was reached. Initial 
spacing was 7 m and this reduced exponentially to 2 m. Final results 
of the effectiveness of the lines are not known, but Rutley reported a 10% 
reduction in average speed during the day and a 197o reduction at night at 
one site and a 167, reduction in the 85th percentile and 87 reduction in 
the average speeds at another. 

Although speed is the single most important factor in skids, the 
amount of lateral movement of a vehicle in its lane is also important; other 
things being equal a vehicle that moves laterally more than another will 
have a higher probability of getting into a skid situation. There is some 
evidence that adding edge lines decreases variability of lateral movement. 
Conley and RothlZ' found that adding edge lines plus white post delineators 
decreased erratic vehicle movements when used with color coding for ramps. 
Czar and Jacobs—' reported that edge lines decreased lateral placement 
variability while David—' showed that freshly painted center lines also 
reduced it. 



222 



Thus, adding edge lines apparently does not affect vehicles' 
speeds but more dramatic delineation treatments can affect speed at least 
in certain specific cases. Of special interest is the finding that trans- 
verse lines painted on pavement can reduce speed. The theory behind this 
is that speed cues come from perceived motion of objects in the peripheral 
field, and that causing these cues to appear to stream past at an abnor- 
mally fast rate should increase apparent speed and thus lead drivers to 
reduce actual speed. There is no reason why this technique could not be 
used in many different situations such as curves, downhill slopes, traffic 
circles, and T~intersections. It is also possible that exponential patterns 
could be painted at the edges or center of driving lanes or arranged in 
posts or other markers beside the highway. The patterns could be placed 
on the pavement as a kind of rumble strip; the cues here would not be 
visual but should affect drivers the same way since slowing down is asso- 
ciated with pavement segments being felt farther and farther apart. 

6. Instrumentation : This topic deals with speed regulation 
through stimuli provided by instruments on the vehicle. Thus far only the 
speedometer has been considered. In one study, Ritchie, Howard, Myers, 
and Nataraj£2/ showed that subjects who drive without a speedometer 
drove faster than subjects who drove with one. Rutley61/ tested sub- 
jects with a head-up display (HUD) of speed. When a HUD is used, informa- 
tion is projected onto the windshield of a vehicle through collimated light 
so that the image is focused at infinity. The operator sees the image at 
his farthest fixation point with the result that he does not have to change 
focus when looking into the distance as he does when flying or driving. 
Rutley found that 85th percentile speeds were reduced in curves by 5 to 10% 
depending on the vehicles' speed, and that drivers came closer to driving 
at advisory speeds in curves with the HUD than without it. 

7. Conclusions : 

a. Static signs can help control drivers' behavior in certain 
situations but apparently not in others. The reasons for this are complex; 
many factors undoubtedly contribute. A few such as frequency, message 
content, and relevancy have been found to be important. Of these, the 
single most important is probably relevancy; if drivers think a sign's 
information does not conform accurately and realistically with real-world 
conditions, they ignore it. Motivation is another factor; drivers moti- 
vated to look for signs see nearly all whereas they miss many if not moti- 
vated. 



223 



The suggestion that emerges from this is that each sign must be 
precisely tailored to fit each situation it is placed in. This is done 
now to a certain extent of course, but the reviewed studies showed that 
driver behavior was not affected in many cases, indicating that something 
was done incorrectly. Also, the fact that drivers see strikingly small 
percentages of signs in many cases indicates incorrect fits. It should 
be relatively easy to develop signing criteria from behavioral work, e.g., 
questionnaires would certainly provide much useful data and on-the-spot 
evaluation by panels of drivers would do the same. 

b. Dyanmic signing is more effective than static signing. Studies 
indicate speed reductions from 11 to 50% when this kind of presentation is 
used. One reason for success undoubtedly stems from the fact that in many 
cases signs are activated under certain specific conditions such as ice or 
fog. This increases the relevancy of the sign and thus drivers pay more 
attention to it. Another reason is that dynamic signs have more attention- 
getting value if designed with a reasonable amount of care. 

c. Delineation can help regulate speed and variability. Speeds 
at the end of four-lane roads can be reduced at least 10% in the daytime 

and 197o at night using transverse lines, and by unspecified amounts on 
freeway exit and entrance ramps through use of elaborate combinations of 
colors, edge lines, and post delineations. It would be interesting to 
test dynamic delineation techniques for their ability to help regulate 
behavior. If results similar to those obtained from signing are found, 
dynamic delineation should provide much more effective control than static 
delineation. 

d. A vehicle's instruments can also influence speed and hence 
skid potential. With a HUD, speed in curves can be reduced by at least 

5 to 107 o . It is difficult to think of head-up display as a practical 
technique because it is difficult to do, at least at the present, and thus 
would not be economically feasible. It is possible, of course, that 
research and mass production could eventually reduce costs to an acceptable 
level . 

e. The literature reviewed here shows that most driver behavior 
studies have tried to determine how behavior is affected at special sites 

like intersections by using specific stimuli like signs. Very little work 
exists that deals with factors that affect behavior generally, over long 
periods of time. The exception to the latter is work that seeks to deter- 
mine the effects of changes such as marking the edges of roads or displaying 
vehicle information in novel ways such as on the windshield. Unfortunately, 
this work has either yielded negative results or positive results difficult 
to do anything about. 



224 



If the skid reduction problem is thought of as a specific one, 
i.e., one in which it is desired to reduce speeds at special sites, the 
data are encouraging. Speeds can be reduced, especially with dynamic 
signing, and it should be very possible to do it under wet highway or 
other conditions that increase skid potential. Whether or not the speed 
reduction that can be achieved is sufficient to lower the skid potential 
to a safe level is another matter, one that ultimately will have to be 
subjected to experimental test. 

If the skid reduction problem is thought of as a general one, 
i.e., one in which it would be desirable to reduce speeds of vehicles 
over long stretches of road, the data are not so encouraging. In this 
case the simplest procedure would be to train drivers to recognize poten- 
tial skidding conditions and what to do if they do skid (this would apply 
as well to the specific case just discussed). If more direct control is 
desired, new techniques will have to be developed. These might range 
from series of signs placed along the road that are activated when the 
road is wet enough to decrease its skid resistance below a critical value 
and that display various warning messages when activated, to delineation 
treatments similarly activated. It might also be possible to build vehicles 
so that they seem to go faster when the road is wet; it is a fairly common 
experience to slow down when large puddles are encountered suddenly and 
unexpectedly on a wet highway. 



OU.S. GOVERNMENT PRINTING OFFICE: 1971 633-710/44<? 1-3 

225 



FEDERALLY COORDINATED PROGRAM OF HIGHWAY 
RESEARCH AND DEVELOPMENT (TCP) 



The Offices of Research and Development of the 
Federal Highway Administration are responsible 
for a broad program of research with resources 
including its own staff, contract programs, and a 
Federal-Aid program which is conducted by or 
through the State highway departments and which 
also finances the National Cooperative Highway 
Research Program managed by the Transportation 
Research Board. The Federally Coordinated Pro- 
gram of Highway Research and Development 
(FCP) is a carefully selected group of projects 
aimed at urgent, national problems, which concen- 
trates these resources on these problems to obtain 
timely solutions. Virtually all of the available 
funds and staff resources are a part of the FCP, 
together with as much of the Federal-aid research 
funds of the States and the NCHRP resources as 
the States agree to devote to these projects."" 



FCP Category Descriptions 

1. Improved Highway Design and Opera- 
tion for Safety 

Safety R&D addresses problems connected with 
the responsibilities of the Federal Highway 
Administration under the Highway Safety Act 
and includes investigation of appropriate design 
standards, roadside hardware, signing, and 
physical and scientific data for the formulation 
of improved safety regulations. 

2. Reduction of Traffic Congestion and 
Improved Operational Efficiency 

Traffic R&D is concerned with increasing the 
operational efficiency of existing highways by 
advancing technology, by improving designs for 
existing as well as new facilities, and by keep- 
ing the demand-capacity relationship in better 
balance through traffic management techniques 
such as bus and carpool preferential treatment, 
motorist information, and rerouting of traffic. 



* The complete 7-volume official statement of the FCP is 
available from the National Technical Information Service 
(NTIS), Springfield, Virginia 22161 (Order No. PB 242057, 
price .$45 postpaid). Single copies of the introductory 
volume are obtainable without charge from Program 
Analysis (HRD-2), Offices of Research and Development, 
Federal Highway Administration, Washington, D.C. 20590. 



3. Environmental Considerations in High- 
way Design, Location, Construction, and 
Operation 

Environmental R&D is directed toward identify- 
ing and evaluating highway elements which 
affect the quality of the human environment. 
The ultimate goals are reduction of adverse high- 
way and traffic impacts, and protection and 
enhancement of the environment. 

4. Improved Materials Utilization and Dura- 
bility 

Materials R&D is concerned with expanding the 
knowledge of materials properties and technology 
to fully utilize available naturally occurring 
materials, to develop extender or substitute ma- 
terials for materials in short supply, and to 
devise procedures for converting industrial and 
other wastes into useful highway products. 
These activities are all directed toward. the com- 
mon goals of lowering the cost of highway 
construction and extending the period of main- 
tenance-free operation. 

5. Improved Design to Reduce Costs, Extend 
Life Expectancy, and Insure Structural 
Safety 

Structural R&D is concerned with furthering the 
latest technological advances in structural de- 
signs, fabrication processes, and construction 
techniques, to provide safe, efficient highways 
at reasonable cost. 

6. Prototype Development and Implementa- 
tion of Research 

This category is concerned with developing and 
transferring research and technology into prac- 
tice, or, as it has been commonly identified, 
"technology transfer." 

7. Improved Technology for Highway Main- 
tenance 

Maintenance R&D objectives include the develop- 
ment and application of new technology to im- 
prove management, to augment the utilization 
of resources, and to increase operational efficiency 
and safety in the maintenance of highway 
facilities. 



DOT LIBRARY 




0017^2^1=.